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Full text of "Alfred Weber's theory of the location of industries"





























In presenting this book to the public I am spared an embar- 
rassment that many writers encounter ; I do not need to give an 
apology for the topic with which it deals. Alfred Weber's treat- 
ise is a pioneering venture. He attempts to master by theoreti- 
cal analysis a complete wilderness of facts which has grown up 
around us during the last two centuries concerning the location 
of our modern manufacturing industries. To be sure, others 
have ventured upon the task of describing and classifying the 
phenomena of geographical distribution; but, as Weber points 
out, previous writers did not get beyond a mere enumeration of 
various factors which played a part in determining the location 
of industries. 

While I am quite impressed with the importance of Weber's 
work itself, if clearly understood, it is precisely this task of mak- 
ing it understood about which I feel very apologetic. In spite of 
the help and advice which Professors Leon C. Marshall and 
Frank W. Taussig, as well as Drs. E. H. Chamberlin, William 
Y. Elliot, Edward Mason, Talcott Parsons, and Andreas Pre- 
döhl have so generously afforded me, I do not feel confident 
that I have succeeded in conquering the difficulties which con- 
front the translator of such a highly abstract treatise. Had not 
Professor Marshall and Dr. Mason read the entire manuscript 
through and made numerous suggestions for its improvement, I 
fear I should not have found the courage to let it see the light of 

It will be conceded by those who have embarked on the 
hazardous adventure of translating abstract thought from one 
language into another that nothing is more perplexing. It is in 
such thought that the Sprachgeist develops its subtlest distinc- 
tions, successfully defying either translating, transcribing, or 



paraphrasing. For this reason the paging of the German edition 
of Weber's book has been inserted as marginal notes through- 
out. These notes are usually inserted at the end of a sentence, 
even though that sentence overlaps the page in the original. 
The interested reader will consult the German text wherever 
the English translation becomes too obscure. Had space per- 
mitted, I should have included the German text itself. But, 
after all, the greatest usefulness of such a translation is the as- 
sistance it may give to the student who knows the original lan- 
guage, but does not know it sufficiently well to enable him to 
make the entire translation himself. 

Comparison with the German text will show that Weber's 
preface to the first and second (unaltered) edition, as well as his 
two notes (Exkurse) have been omitted. We should have been 
glad to include Weber's contribution to the Grundriss der So- 
zialökonomik^ could it have been arranged. I can only refer to 
this treatise all readers who are particularly interested in those 
aspects of location which Weber touches upon in his introduc- 
tion and in his last chapter as well as in the paragraphs through- 
out the book on tendencies of development. It seemed impor- 
tant to include the mathematical appendix by Georg Pick. I sin- 
cerely hope that the indulgent reader will not feel as did that stu- 
dent who wrote on top of Alfred Marshall's mathematical ap- 
pendix to his Principles: ''A bad case of appendicitis — cut it 
out." In translating this mathematical appendix I have had the 
valuable advice of Mr. Paul S. Bauer. 

This study would probably not have been possible without 
the constant encouragement of Professor Leon C. Marshall. I 
wish to thank him and all others who have helped me. 

C. J. F. 

^"Industrielle Standortslehre (Reine und kapitalistische Theorie des Stand- 
orts)," in Grundriss, Abteilung VI, B, particularly the second part dealing with 
capitalistic theory. 



Editor's Introduction: The Theory of Location in Relation to 

THE Theory of Land Rent xiii 

1. In John Stuart Mill xiii 

2. In Alfred Marshall . . . . " xv 

3. In J. H. von Thiinen xix 

4. In Alfred Weber xxii 

5. Significance for a Theory of Monopoly, Transportation Rates, 

and International Trade . xxix 

Author's Introduction i 

1. Importance of an Economic Theory of Location .... i 

2. Limitation to a Theory of the Location of Manufacturing 
Industry; Reasons Therefor 4 

3. Method Employed 8 

4. Limitations of the Results 12 

Chapter I. LocATioNAL Factors and LocATiONAL Dynamics 17 

I. The Terms "Locational Factor" and "Locational Unit" . 17 

IL Classification of Locational Factors 20 

a) General and Special 20 

b) Regional and Agglomerative 20 

c) Natural and Technical, Social and Cultural .... 21 

III. Ascertaining the General Factors of Location .... 23 

a) Ascertaining the Individual Regional Factors ... 23 

b) Costs of Transportation and Labor Costs Are the Only 
Regional Factors 29 

IV. Theory of the Locational Factors 34 

Chapter II. Simplifying Assumptions 37 

I. The Assumption of a Separate Basis of Material Supply, Con- 
sumption, and Labor . 37 

II. The Consideration of the "Forces of Nature" 39 

Chapter I^I. Transport Orientation (Transportorientierung) 

Section I. Analysis of Transportation Costs 41 

I. Weight and Distance the Only Elements of Cost in Our 

Theoretical Analysis 41 




2. The Type of the Transportation Sj^stem and the Extent of 

Its Use 43 

3. The Nature of the Locality and Its Kinds of Roads . . 45 

4. The Nature of the Goods 45 

5. Relation to Reality 46 

Section IL The Laws of Transport Orientation 48 

1. The Locational Figures and the Kinds of Industrial 
Materials 48 

2. Mathematical Solution 53 

3. Material Index, Locational Weight, and Theoretical 
Conclusion 59 

4. Cases 61 

5. The Orientation of an Entire Industry 67 

a) The Creation of the Individual Figures .... 67 

b) Co-operation of the Individual Figures .... 70 

6. The Factors of Transport Orientation 72 

7. Tendencies of Development 73 

Section III. Approximations to Reality 76 

1. The Existing System of Transportation Rates ... 76 
A. Deviations from the Pure Calculation of Rates 

According to Mileage 77 

A. Deviation from the Pure Calculation of Rates Accord- 
ing to Weight 78 

2. The Real Nature of the Transportation System ... 81 

A. A Divided System of Transportation 81 

B. Different Kinds of Transportation Systems Working 
Together 82 

a) The Effect of the Waterways 84 

b) The Effect of the Net of Highways 86 

3. Further Applications of the Theory to Reality ... 88 

A. The Price Differences of Materials and Their Effect . 88 

B. The Use of Water Power . . 89 

a) The Use of Waterfalls 89 

b) Transmissible Water Power 91 

Chapter IV. Labor Orientation 95 

Section L The Analysis of Labor Costs 95 

1. The Geographical Differences in Labor Costs 95 

2. Their "Forms of Occurrence"; Differences Accordini7 to 
Area 97 

3. Simplifying Assumptions 100 



Section II. The Law of Labor Orientation 102 

1. Theoretical Solution; Isodapanes 102 

2. The Conditions of Labor Orientation 105 

3. The Character of the Industries and Labor Orientation 107 

A. Orientation of an Individual Plant: Index of Labor 
Costs and Coefficient of Labor 107 

B. Orientation of an Entire Industry: Elimination of 
Labor Locations and Replacement of Deposits . 112 

4. The Environmental Conditions of the Labor Orientation 117 

5. Tendencies of Development 120 

Chapter V. Agglomeration 124 

Section I. Analysis of Agglomerative and Deglomerative Factors 

1. Object of the Analysis 124 

2. Definitions: Function of Economy and Function of 
Agglomeration 126 

3. Agglomerative and Deglomerative Factors . . 127 

A. Agglomerative Factors 127 

a) Development of the Technical Equipment . 128 

b) Development of the Labor Organization 129 

c) Marketing Factors 130 

d) General Overhead Costs 130 

B. Deglomerative Factors 131 

Section IL The Laws of Agglomeration 134 

A. Agglomeration within Transport Orientation 135 

1. Agglomeration with Fixed Index 135 

a) When Does Agglomeration Take Place, and How 
Much? 135 

b) Where Will Agglomeration Take Place? .... 138 

c) The Size of the Unit of Agglomeration 139 

d) Modifications 141 

2. Agglomeration in the Case of an Increasing Index . 143 

3. The Conditions of Agglomeration 147 

4. The Formula of Agglomeration 153 

B. Agglomeration and Labor Orientation 156 

Section HI. Reintroducing the Realities 162 

1. Coefficient of (Value Added through) Manufacture 
(Formkoeffizient) 162 

2. The Forms of Agglomeration in Reality 166 

3. Tendencies of Development 168 



Chapter VI. The Total Orientation 173 

Section I. The Organization of the Stages of a Given Productive 

Process 174 

A. The Stages of Production and Transport Orientation 174 

1. When Does a Split Occur in the Production? . 174 

2. Where Will the Locations of the Productive Stages Be 
When Production Is Split? 178 

3. A More Precise Answer to the Question: When Does a 
Split in the Production Occur? 182 

4. Complications (Replacement of Material Deposits) . . 183 

B. The Stages of Production and Labor Orientation . 184 

C. The Stages of Production and Agglomeration .... 186 

D. Reintroducing the Realities 187 

1. General Observations 187 

2. Tendencies of Actual Development 190 

Section II. The Interaction of the Independent Productive 

Processes 196 

1. The Coupling of Independent. Productive Processes . 197 

2. Connection through Materials 201 

3. Market Connection 206 

4. The Total Orientation 209 

Chapter VII. Manufacturing Industry within the Economic 

System 211 

Introductory Remark 211 

I. Historical Distribution of Locations 213 

IL The Strata of Locational Distribution and Their Interaction 214 

III. The Result and the Remaining Problem 221 

Mathematical Appendix, hy Georg Pick 226 

Introductory Remark 227 

I. The Locus of the Least Costs of Transportation . 227 

IL Curves of Equal Transportation Cost 240 

HI. Agglomeration 245 

Index 253 




"Knowledge insufficient for prediction may be most valua- 
ble for guidance," wrote John Stuart Mill, in discussing eco- 
nomic theory in general.^ This statement might very properly 
have been made the motto of Weber's attempt to analyze a 
much-neglected problem by what Mill would have called a strict- 
ly deductive method. This problem is: what causes an indus- 
try^ to change its location? 

The change of industrial location is among the most gener- 
ally discussed economic problems of today. In the nation-wide 
agitation for power development in the United States, for ex- 
ample, the argument is quite generally used that it will ''decen- 
tralize" industries.^ English economic theory, however, has neg- 
lected a strictly theoretical analysis of the problem. From 
Adam Smith to Pigou no adequate deductive treatment of the 
causes determining economic location has been attempted, in 
spite of the fact that such an analysis may be capable of aiding 
in further refining the theories of monopoly, transportation rates, 
and international trade. 

John Stuart MilP touches upon the problem when consid- 

" Logic, Book 6, chap, ix, §2. 

^ "Industry" is used here and throughout in the sense of manufacturing in- 
dustry, unless stated otherwise. 

*So Secretary Hoover. Compare his address at the First International 
Power Conference, London, 1927, Prosperity Through Power Development. 
Compare also the many generalizations which are made in order to explain the 
movement of industries to the South, 

"It is, of course, arbitrary to begin with Mill, but it may be justified on 
grounds of expediency, since he more or less systematized and correlated the 
thought of those before him. I, for one, should Hke to include at least Adam 


ering value. In enumerating the various channels through which 
labor cost influences the cost of production he, like previous 
writers, includes the cost of transporting materials to the place 
of production and the cost of '^conveyance of products to the 
market."*^ But he does not consider the variability of this factor 
as affecting the place of production, although some of the direct 
effects of purely locational factors did attract his attention. "Al- 
most all kinds of raw material extracted from the interior of 
the earth — metals, coals, precious stones, etc., are obtained from 
mines differing considerably in fertility, that is, yielding very 
different quantities of the product to the same quantity of labor 
and capital." But he apparently despaired of explaining this 
phenomenon, since he goes on: "Whatever the causes, it is a fact 
that mines of different degrees of richness are in operation, and 
since the value of the produce (the costs) must be proportional 
to the cost of production at the worst mine (fertility and situa- 
tion taken together), it is more than proportional to that of the 
best."' Here "situation" (which corresponds to our term "loca- 
tion") emerges for a moment as a factor, but immediately dis- 
appears again behind the more usual consideration of "fertility." 
But this factor of "location," whose determining causes seem so 
elusive to Mill, may be capable of rational explanation if only 
we carry our inquiry one step farther and analyze the factors 
which determine what is and what is not a "favorable" location. 
We shall return to this point presently. It remains to call atten- 
tion here to the fact that the passages just discussed appear in 

Smith and Ricardo, because of their relation with the system of Von Thiinen. 
But the pecuharities of their theories of rent would require too much time to 
review for the particular problem in hand (cf. Schumpeter, Epochen der Dog- 
men-und Methodengeschichte, pp. 87 ff.). It is not very difficult, moreover, to 
apply what is here said about John Stuart Mill to the earHer thinkers. 

^Principles (New York, 1874, from the sth London edition). Book III, 
chap, iv, §1. In succeeding notations Roman numerals refer to book, Arabic to 
section, unless otherwise indicated. 

''Principles, III, chap, v, 3. The itahcs are mine. 


connection with Mill's analysis of rent in its relation to value. It 
may not be amiss to quote another passage which may shed more 
light upon this aspect of the matter: ''Land is used for other pur- 
poses than agriculture, .... and when so used yields a rent. 
.... The ground rent of a house in a small village is but little 
higher than the rent of a similar patch of ground in the open 
fields, but that of a shop in Cheapside^ will exceed these, by the 
whole amount at which people estimate the superior facilities of 
money-making in the more crowded place."^ But all this hardly 
explains why Cheapside came to be Cheapside ! Why did Cheap- 
side happen to become a "favorable" location? A theory of lo- 
cation will consider the situation or location rent a problem 
rather than merely a fact, and therefore the theory of location 
may serve as a fruitful avenue of approach to certain obscure 
aspects of the theory of rent, value, and distribution. We shall 
have occasion later to indicate briefly how it becomes important 
for the theory of monopoly, for the theory of international trade, 
and for the theory of railway rates. While it would be interest- 
ing to consider here Mill's analysis of the influence of the prog- 
ress of industry upon rents,^^ we shall have to content ourselves 
with a mere mention of the problem and proceed to a few obser- 
vations upon the position of Alfred Marshall. 

The strong interest of Marshall in production naturally led 
him to touch upon the question of what causes the location (or, 
as he called it, ''localisation") of industries to change. From the 
point of view of anyone interested in the history of economic 
ideas in general and in the history of the theory of location in 
particular it is quite interesting that Alfred Marshall (in the in- 
troduction to the first edition of his Principles of Economics) 
acknowledges his great indebtedness to Thünen. It will be re- 
membered that it was Thünen who advanced a theory of the lo- 

^ An expensive trading section in London. 
^Principles, III, chap, v, 3; cf. also III, chap, v, 4. 
^" Principles, IV, chap. iii. 


cation of agricultural production/^ But while Thünen related 
his theory very definitely to his theory of rent, modifying the 
position of Adam Smith/" Marshall did not approach this prob- 
lem of location from a theoretical point of view, and consequent- 
ly attempted no answer to that aspect of the theory of rent which 
we have just pointed out. There is a twofold explanation for this. 
For one thing, Marshall's main effort was directed toward work- 
ing into the theory of rent the supposedly new equilibrium theory 
of demand and supply,^^ contenting himself with carefully restat- 
ing the theory that ''rent does not enter the cost of production,"^* 
Marshall does not inquire into the problem which he, like Mill 
before him, encounters. In discussing the argument which arose 
between Ricardo and Smith regarding the ''price at which coals 
can be sold for any considerable time,"^^ he is inclined to agree 
with Ricardo that "it is the least fertile mine which regulates the 
price." Omitting the matter of a royalty which enters on account 
of the exhaustibility of a mine, Marshall, like Mill, does not ex- 
plain why a less fertile mine should be in use at all. Like Mill, 

" Der Isolierte Staat, particularly Part I. For a recent interpretation of the 
significance of this treatise in the history of economic thought, cf. Edgar Salin, 
"Der Isolierte Staat 1826-1926," in Zeitschrift für die gesamte Staatswissen- 
schaft, 1926. 

" He made the distinction between rent of land and profit on capital in- 
vested on the land, like Ricardo. 

" While this name was not used by Mill, the essential aspects of the con- 
cept of "equilibrium," as far as they matter for the problem here in hand, were 
treated by Mill as indicated above, 

" It is stated as follows : "When land capable of being used for producing 
one commodity is used for producing another, the price of the first is raised by 
the consequent limitation of its field of production. The price of the second will 
be the expense of production (wages and profits) of that part of it which only 

just pays its way And if for the purposes of any particular argument we 

take together the whole expenses of the production on that land, and divide these 
among the whole commodity produced, then the rent, which ought to count in, 
is not that which the land would pay if used for producing the first commodity, 
?)Ut that which it does pay when used for producing the second" {Principles, 4th 
ed., p. 483). 

" Cf. loc. cit., p. 484. 


he speaks of the fact that a rise in rent may cause a manufac- 
turer to move into another town or into the country, but he does 
not say why the rent does rise in the first instance. Similarly, he 
explains that the demand for exceptionally valuable urban land 
comes from traders of various kinds, wholesale and retail, more 
than from manufacturers. But why such increase in the demand 
should come, he does not explain at all. Still, the most striking 
instance where Marshall encounters the problem of location (or 
situation) without undertaking to solve it is in his discussion of 
what he calls situation rent.^^ 

If in any industry, whether agricultural or not, two producers have 
equal facilities in all respects, except that one has a more convenient situa- 
tion than the other, and can buy or sell in the same markets with less cost 
of carriage, the differential advantage which his situation gives him, is the 
aggregate of the excess charges for cost of carriage to which his rival is put. 
And, we may suppose, that other advantages of situation, such, for instance, 
as the near access to a labour market especially adapted to his trade, can be 
translated in like manner into money values. When this is done for, say, a 
year, and all are added together we have the annual money value of the ad- 
vantages of situation which the first business has over the second; and the 
corresponding difference in the incomes derived from the two businesses is 
commonly regarded as a difference of situation rent}"^ 

But why does not the second manufacturer move to the more 
favorable location? This fact certainly needs an explanation! 
In a footnote Marshall refers to two examples, in both of which 
the competitive position of two productive units is the same 
because the additional cost of production due to capital and 
labor of one are compensated for by the more favorable loca- 
tion of the other in relation to the market. "Favorable loca- 
tion" in both cases refers to advantages in transportation costs. 
But these, obviously, are not examples of production which 
have any bearing upon the problem of location, because when 

^^ Principles, V, chap. x. 

" The italics in this quotation are mine. 


locational advantages of one kind (labor, etc.) are balanced by 
locational advantages of another, no change of location will take 
place. On the other hand, it is not clear how the advantage due 
to reduced transportation costs can be called a "rent," since it 
is not explained why the other productive unit is not quite free 
to go to a place with the same balance of advantage/* Feeling 
perhaps the inconclusiveness of his reasoning, Marshall pro- 
ceeds to treat of "exceptional cases in which the income derived 
from advantageous situation is earned by individual effort and 
outlay." Much of this uncertain generalizing could have been 
subjected to rational explanation by an adequate understanding 
of the underlying locational problem. It remains to say a word 
regarding certain forms of quasi-rent (as Marshall called it) 
which are due to the fact that a certain location is made more 
favorable by environmental factors. The true nature of rents of 
this kind, which are due to a disturbed equilibrium of loca- 
tions, becomes recognizable only if the locational network of 
the underlying regular stratum of locations is distinguished 
quite clearly. 

Marshall's reluctance to undertake their analysis in con- 
nection with these rent problems does not, however, prevent him 
from treating "the concentration of specialized industries in 
particular localities."^^ But what he gives is, as Alfred Weber 
pointed out later, a more or less systematic survey of various 

^*The actual examples refer to extractive industries. These involve the 
question of increased output, as did the example of Mill we have cited. It is 
curious that Marshall should at this point quote Thünen's Der Isolierte Staat 
with outspoken approval, while failing to make use of Thünen's theory of loca- 
tion contained therein. 

" Principles, IV, chap. x. Cf . also his interesting discussion in Industry and 
Trade (1923), chap, ii, and elsewhere, where he quotes Alfred Weber (p. 27). 
But it seems rather doubtful whether he appreciated the full significance of 
Weber's theory, since he says of it that it is a development of Lardner's Law of 
Squares in transport and trade (as set forth in Railway Economy [1850], p. 14). 
The connection is rather far fetched, to say the least. 


locational factors; but — much like Roscher-^ — ^he does not in 
any way develop or even employ the theoretical concepts which 
Thiinen had first worked out. This is rather interesting (or shall 
I say astonishing?) in view of the close relation between him 
and Thiinen. But, as has been noted before, Marshall seems 
mainly concerned with working into the classical system the 
new equilibrium theory which is also to be found in Thiinen. 
Marshall was probably too deeply concerned by the "psycholog- 
ical" foundation which he and others had given to that theory 
to be willing to bother with Thiinen 's concept of an isolated eco- 
nomic system.^^ It may be helpful, therefore, to sketch in a few 
sentences the main outline of Thiinen's theory of location,^^ al- 
though it involves in some respects repeating what is known to 
economists in connection with his theory of rent. 

Thiinen, like Ricardo, studied an imagined state of facts in 

^**W. Roscher, Studien ueber die Naturgesetze, welche den natürlichen 
Standort der Industriezweige bestimmen. Similar catalogues of possible factors 
have been published by others, compare, for example, F. S. Hall, "The Localiza- 
tion of Industries," Twelfth Census, Manufacturers, Part I ; and Edward A. Ross, 
"The Location of Industries," Quarterly Journal of Economics, X (1896), 247 ff. 
For a discussion of these and many other minor contributions cf. Witold Krzy- 
zanowski, "Literature of Location of Industries," in Journal of Political Econ- 
omy, XXXV (1927), 278 ff. 

^^ It is rather hard to withstand the temptation to take up this aspect in the 
history of economic thought in greater detail ; but such an undertaking could not 
be given justice within the scope of this brief essay. Similar considerations com- 
pel me to pass over without more than a casual reference the difficult problems 
which arise from the twelfth chapter of the sixth book of Marshall's Principles 
where he deals with the influence of progress on value. Such further discussion 
would have afforded an opportunity to consider the work of some of the writers 
of the next generation, particularly A. C. Pigou and J. M. Clark (Principles of 
Overhead Costs). 

^His theory is to be found in Der Isolierte Staat, 2d ed., 1842, and later. 
Edgar Salin, writing upon the history of economic theory, expressed the belief 
that Thiinen was the most important German theorist of the nineteenth century. 
However, the part of his system in which he expounds his theory of location has 
least been heard of and is seldom referred to in any theoretical treatises written 
in English. Not even special studies such as that of Ross mentioned in footnote 
20 above, seem to have been aware of it. 


which all nonessential aspects of the real case have been elimi- 
nated. In his totally isolated economic system-^ he finds that the 
location of different kinds of agricultural production is deter- 
mined by the relation between the price of the products in the 
market place and the distance from the market place. The most 
significant result of this approach to the problem is that the cost 
of transporting the products to the market place is isolated as the 
basic element and made the starting-point of the analysis of lo- 
cation. It is possible to do this because it is supposed anyway 
for the purpose of this analysis that labor cost (wages) are equal 
throughout the plain.^* Besides, equal fertility is assumed 
throughout. It is worth noting that Thünen does not consider 
the effect of the cost of transporting appliances (such as plows, 
etc.) to the place of production. This omission unduly simph- 
fies his analysis as compared with that of Alfred Weber. But it 
should not be forgotten, anyhow, that the theory of location of 
Thünen was the by-product of quite a different problem, name- 
ly, "how will the kind of agricultural production of a certain 
farm be affected by a gradual decline of the prices of its produce 
in its [fixed] market" ?^^ It is well known that Thünen finds 
rent to be due primarily to the advantage which is caused by a 
smaller distance from the consuming center, i.e., smaller costs 
of transportation.^^ This finding is based upon the law: 'The 
value of produce at the place of production decreases with the 
distance of the place of production from the market place.""^ 

^^ The picture of this system is well-known. He supposes a town (market 
place) within a fertile plain, without navigable rivers or canals, and of given fer- 
tility throughout, which ends somewhere far away from the town in the wilder- 
ness. Thünen himself calls this ". . . . eine bildliche Darstellung, eine Form, die 
den Ueberbhck erleichtert und erweitert; die wir aber nicht aufgeben dürfen, 
weil sie, wie die Folge ergeben wird, so reich an Resultaten ist." 

^This supposition, while not expressly made in the first part, is noted by 
Thünen in the third part, p. 73. 

^ Der Isolierte Staat, I, p. 21. 

"* Op. cit., p. 227. '' Op. cit., p. 37. 


But Thiinen was, of course, well aware of the fact that this is not 
a complete explanation of rent. In the third part of his work he 
finds rent based upon differences in the wage level. This second 
explanation seems to contain a contradiction to the first. Such 
seeming contradiction is due to different premises; in the one 
case it is assumed that the wage level is constant; in the other, 
that the value of the produce is constant, i.e., that cost of trans- 
portation is constant (according to the rule just cited). It is 
possible to assume this theoretically in spite of the fact that the 
wage level is changing — indeed, this possibiHty is of central im- 
portance for all that follows. This second assumption that the 
value of the produce is constant further involves the assumption 
that no more uncultivated soil is available. In the first case, 
then, the value of the produce is the variable, dependent upon 
the larger or smaller costs of transportation to the market place. 
In the second case, the wage level is the variable. What is com- 
mon to both cases is that the cost of production does not rise in 
proportion to the value of the produce, so that if the value of the 
produce rises above a certain point there remains a surplus 
which is the basis of a rent.^^ Expressing this finding in relation 
to the main problem before referred to, Thiinen formulates 
(stated with slight alterations for the present purpose) that the 
price of the produce must be so high that the rent of that farm 
for which it is most expensive to transport the produce to the 
market place does not become less than zero. Unfortunately, 
Thunen did not work out the significance of this second aspect 
for his implied theory of location. It would have been necessary 
to analyze the variations produced by the introduction of this 
second factor: labor cost. Had he done so, his theory would be 
more clearly related to that of Alfred Weber. It will be ob- 
served that Thunen, considering agricultural production only 
(an extractive industry), assumes here a definite and constant 
limit of production at any given place (so and so many bushels 

^Der Isolierte Staat, I, p. 73. 


of wheat per acre, for example). The validity of this assump- 
tion is, even in agriculture, subject to the further assumption 
^ that the most intensive methods are already in use equally 
throughout. Such an assumption would not be in accord with the 
generally accepted modern doctrine of the variability of produc- 
tive forces. Be this as it may, such supposition has obviously 
no significant application to manufacturing industries. It is, on 
the contrary, possible to assume that a practically unlimited 
amount of one kind of production may be carried on at one place 
rather than another. More of this later. 

I have said before that Thünen's theory of agricultural loca- 
tion was a by-product of his effort to determine which kind of 
production would best be carried on at a given place. Alfred 
Weber, on the other hand, undertakes the analysis of industrial 
location for its own sake.^^ It is useful to bear this difference in 
mind. Observing the gigantic movements of manufacturing in- 
dustries, Weber asks: What causes a given industry to move 
from one location to another? What are the general economic 
laws determining these movements ? Theoretically, Weber, like 
Thiinen, might have asked: Which industry should be carried 
on at any given place? But, as a matter of fact, such an ap- 
proach to the problem appears mistaken at first sight because 
the possibilities of manufacture are legion. This point reveals a 
third limitation of Thünen's analysis: he assumes a very limited 
group of products, namely, the agricultural produce of German 
farms in the beginning of the nineteenth century. This made it 
possible for him to find a reasonably satisfactory answer to his 
question, what kind of production would best be carried on at a 

^ Alfred Weber, TJeber den Standort der Industrien, I. Teil, Reine Theo- 
rie des Standorts, and Alfred Weber, "Industrielle Standortslehre (Allgemeine 
und kapitalistiche Theorie des Standorts)," in Grundriss der Sozialökonomik, 
Abteilung VI, B. The few points which are emphasized here are chosen with ref- 
erence to the focusing point of this essay, rent. They do not propose to describe 
the theory itself. That will best be understood from Weber's own work. 


given place. But this answer is satisfactory only within the lim- 
its just indicated. 

Weber, who concentrates upon the problem of location as 
such, is not hampered by this limitation. He, of course, is in- 
terested only in discovering the operation of such general fac- 
tors as influence manufacturing industries. But before going 
into the questions connected with that issue, it may be useful to 
compare the theoretical picture from which he starts with that 
of Thünen. Like Thiinen, he assumes an absolutely even plain 
and equal transportation rates throughout. But he does not as- 
sume one consuming center; he assumes many of them scat- 
tered over the plain. Instead of equal fertility throughout, 
which would correspond to equal amounts of fuel and raw mate- 
rials at equal cost throughout, Weber assumes only equal cost / 
of fuel and raw materials at all deposits,^^ but retains the un- 
even distribution of such deposits. These, and these only, are 
Weber's assumptions. 

The variable general factors are of two kinds : those which 
are primary causes of the regional distribution of industry (re- 
gional factors), and those which are secondary causes of a re- 
distribution of industry (agglomerating and deglomerating fac- 
tors), being themselves effects of those regional factors. By ana- 
lyzing one given industrial process Weber deductively finds two 
general regional factors of cost: transportation costs and labor 
costs. It might be objected here that transportation costs are 
themselves partly determined by labor costs. This is true; but 
it is essential for the analysis of location to isolate costs of trans- 
portation as a separate element, since the problem of location is 
one of spatial distribution. The term ''labor costs" is therefore 
used here and elsewhere in the sense of labor costs as applied to 

^" When Weber wishes to express possible differences in the price of fuel and 
raw materials at different deposits by additions to the distance between them 
and the place of production, this amounts theoretically to assuming equal cost 
of fuel and raw material throughout at their deposits, since the theoretical prem- 
ises contain no assumption regarding the "real" distance of any point. 



a given industry. This simplification is justified by the fact that 
Weber's problem is: What causes a given industry to move/ 
from one location to another? It is even possible to assume va- 
riations in the wage level (labor costs) of such a given industry 
without necessarily implying a change in the labor costs of any 
other industry, like the transporting agency. Apparently these 
are exactly the same factors which Thünen had found. But, un- 
like Thünen, Weber analyzes the effects of a change in both 
variables. After having ascertained the laws determining the lo- 
cation when labor costs are constant, he proceeds to ascertain 
the alterations resulting from varying costs of labor. He is able 
to formulate his result in definite rules. Firstly, he finds that the\/ 
location of manufacturing industries is determined (transporta- 
tion costs being variable, labor costs constant) by the ratio be- 
tween the weight of localized^'^ material and the weight of the 
product.^- This ratio Weber calls the material index. The ex- 
planatory value of this general rule need not be discussed here 
in detail.^^ This result was reached upon the assumption of 
equal labor costs throughout. What variations will be caused 
by varying costs of labor? Weber finds: The extent of the 
variation caused by varying labor costs is determined by the 
ratio between cost of labor per ton of product (labor index) and 
the total weight of all goods (product, materials, fuel, etc.) 

^^ Localized are such materials as are not to be had everywhere ; the latter 
are called ubiquities. Cf. infra, p. 51. An interesting discussion of these concepts 
will be found in Oskar Engländer, Theorie des Güterverkehrs und der Fracht- 
sätze, p. 121 ff. It is convincingly urged there that the decisive point is whether 
a material is to be had everywhere at equal prices. 

^^It is fairly simple to relate this rule to the theory of land rent as it be- 
comes a function of location. A fuller discussion will be undertaken below in 
connection with the indirect general agglomerating and deglomerating factors 
determining the location of manufacturing industries. 

^' By way of illustration, this may be said : Certain materials enter with 
their entire weight into the product (silver, etc.); others not at all (coal, etc.). 
This distinction is of considerable significance. Weber is able to make the for- 
mula that the production of all industries whose material index is not greater 
than I is located at the place of consumption (cf. infra, p. 61). 


transported. This total weight is called locational weight, and 
the ratio just described is called labor coefficient. Now Weber 
can deduce the second general rule: When labor costs are varied, '^ 
an industry deviates from its transport locations in proportion 
to the size of its labor coefficient. 

The writer wishes Alfred Weber had analyzed the locations 
which result when transportation costs are eliminated, before 
studying the variations due to varying labor costs, while cost of 
transportation remained variable.^* The results of such an anal- 
ysis would enable us to check upon the results of the previous 
analysis by introducing transportation costs into a network of 
locations first solely determined by cost of labor.^^ It would 
have served also as an excellent basis of defense against the crit- 
icism of Werner Sombart,'^^ which does not really touch the 
foundation of Weber's theory at all because Sombart does not 
take up the problem from the point of view of economic theory. 
It is not possible to go into details, but the final result of such an 
analysis seems quite obvious. If transportation costs were con- 
stant, all production would go to the locations with lowest labor 
costs. To illustrate this "rule" let us assume that the labor costs 
are equal at A, B, and C, and a given distribution of a given in- 
dustry between A, B, and C exists. If, then, the labor costs at A 
fall, all production will move at once from B and C to A .^^ It 

^ It is necessary for a clear understanding of this discussion to bear in mind 
that an elimination of transportation costs would only result if it were assumed 
that it costs the same to ship goods of any kind and any weight any distance. 

^' It will be remembered that Thiinen made this first step, although incom- 
pletely, due probably to his preoccupation with the problem of rent (cf. above, 
p. xviii). But he failed to carry his analysis beyond this elemental stage and did 
not study either the variations caused by introducing labor costs into a system 
of locations determined by transportation costs or the variations caused by in- 
troducing transportation costs into a system determined by labor costs. 

^ Cf . his review in the Archiv für Sozialwissenschaft und Sozialpolitik, XXX 
(1910), 748, and Der Moderne Kapitalismus, 3d ed.. Vol. II, 2, p. 800, 901 ff. 

'^ It must not be objected here that this is inconceivable, because the "de- 
mand" for labor in A would at once raise the cost of labor in A, since it is an 


would be easy to show that an introduction of transportation 
costs into these simple equations would give results identical 
with those obtained by Weber. Obviously the rule just stated, if 
we should be willing to call it such, has no explanatory value, 
because its application to different industries shows no "typi- 
cal" alterations for each industry,^^ but affects all industries 
ahke; whether they had high labor costs per ton of product, or 
low, they would obviously go to the location which rendered this 
part of their cost lowest. 

The main reason for entering upon the discussion contained 
in the foregoing paragraph is to show that Weber was methodo- 
logically fully justified in starting his analysis with variable 
transportation costs and constant labor costs, because the loca- 
tional significance of variations in labor costs becomes capable 
of analysis only in its relation to the total weight of all goods to 
be transported during the particular process of production. It 
seems to the writer that it is of the greatest importance that Al- 
fred Weber has thus succeeded in laying bare the fact that trans- 
portation costs are theoretically the most fundamental element 
determining location, because it is only in relation to these 
two fundamental figures, the material index and the locational 
weight, that general rules can be stated whose application to 
particular industries shows significant alterations for each in- 
dustry.^^ The only question which arises regarding Weber's de- 
ductions is whether it would not have been better to stick to 
transportation costs as the only ''general" factor of location, 
and to treat labor as an indirect factor. Andreas Predöhl seems 
to be inclined to take this view, although his claim that "there is 

implication of our hypothesis that there is an abundant supply of labor at every 
location at the prevailing wage level. 

^® This may be the reason why Thünen refrained from stating it in relation 
to the problem of location. 

^^This entire reasoning is based upon a theory of theory which chooses 
among different possible theories upon the basis of their explanatory value. 


no logical difference between the labor factor and any other local 
factor" goes too far.*° 

What has been said thus far may suffice to explain the loca- 
tion of industries as affected by factors which are both common 
to all industries (general factors) and direct in their operation. 
But, as was noted before, certain further variations are caused 
by factors which are themselves partly caused by those direct 
or primary (Weber calls them regional) factors just discussed. 
These indirect factors (agglomerating and deglomerating) are 
not capable of the same deductive analysis as the direct fac- 
tors discussed before, because they follow from the social na- 
ture of production. Quite generally speaking, such an indirect 
factor is an advantage which follows from the fact that not 
less than a certain quantum of production is agglomerated at 
one place (agglomerating factor), or from the fact that not 
more than a certain quantum of production is agglomerated at 
one place (deglomerating factor). The agglomerating factors 
(advantages from large-scale production through technical ap- 
paratus, labor organization, etc.) are related to the nature of 
the particular industry, while the deglomerating factors are all 
traceable to the inevitable increases in the rent of land which ac- 
company the agglomeration of industry. 

How far, then, will agglomeration go? The significance of 
an answer to this question for an understanding of rent is ob- 
vious. Let us follow Weber's analysis. He returns to the as- 
sumption of constant labor costs in order to study the deviations 
caused by these agglomerating and deglomerating factors with- 
in the network of locations as determined by costs of transpor- 
tation alone. He eliminates the deglomerating factors by treat- 
ing them as lessening the force of agglomerating factors. But, 

*° Cf. his "The Theory of Location in Its Relation to General Economics," 
Journal of Political Economy, Vol. XXXVI (1928), where he bases his arguments 
to some extent upon Alfred Marshal; and "Das Standortsproblem in der Wirt- 
schaftstheorie," Weltwirtschaftliches Archiv (1925), XXI, where he bases his ar- 
guments upon Gustav Cassel. 


according to Weber, this can only be assumed as long as isolated 
industries are considered; otherwise there exists the possibility 
of ^'accidental" agglomeration of several different industries, 
which would create deglomerating tendencies quite apart from 
an agglomeration of any particular industry.*^ This leads Weber 
to consider the effect of the agglomerating factors upon an iso- 
lated industry, whose locations have been determined by the 
costs of transportation. The economies per ton of product for 
each quantum of agglomeration constitute a function of the ag- 
glomerating factors, the ''function of economy." The increases 
of the economies from quantum to quantum constitute another 
function of the agglomerating factors, the "function of agglom- 
eration." This latter function is the real measure for the extent 
of agglomeration. The extent of agglomeration is determined by 
the ratio between this function of agglomeration and the loca- 
tional weight, the latter multiplied by the (uniform!) rate of 
transportation. Weber finds that a formula exists which shows 
which quantum of agglomeration will be realized.^- 

The reintroduction of variable labor costs shows the two 
"deviating" tendencies, labor and agglomeration, competing 
with each other, with the result that the tendency of industry to 
concentrate at a few locations will be further increased. This 
finding would support our earlier suggestion regarding the posi- 
tion of labor costs within a theoretical treatment of location. 

The foregoing may suffice to show that Alfred Weber and 
Thünen both point out the fundamental importance of trans- 
portation costs for any theoretical understanding of location. 
Hence, upon the basis of the assumptions made in the beginning, 

^ The writer is wondering whether it can even then be assumed. Labor 
costs, we saw, may concentrate a given industry in one or two places which 
would create these deglomerating tendencies. As a matter of fact, even when 
only transportation costs are variable, a concentration of industries in one loca- 
tion may cause a sufficient rise in rent to "deglomerate" them. This was pointed 
out partly and from another point of view by Predöhl, loc. cit. 

*" CL infra, p. 153 Ü. 


rent is capable of analysis as a function of location.^^ It is at 
this point, the writer believes, that the importance of the theory 
of location for general economic theory becomes apparent, for it 
was in connection with this problem that Thiinen developed 
whatever theory of location he did develop. 

Among the problems which have presented major difficulties 
to economic theory, the effect of forces operating to restrain trade 
has occupied a very important place. Monopolies, transporta- 
tion rates, and international tariffs stand out among such forces. 
Their separate theories must necessarily be interrelated. The 
connecting link between them is an adequate theory of rent. 

As to the theory of monopoly, I shall venture no more than a 
hint. A more elaborate discussion would necessitate an analysis 
of the work of at least A. C. Pigou and J. M. Clark.** But one 
thought suggests itself at once: if all deglomerating tendencies 
are related to the rise of land value, i.e., rents, then, where no 
rise in land values becomes apparent (let us say in a socialist 
system), the result would seem to be a considerable acceleration 
of agglomeration.*^ But most economists today would hold that 

*^ Predöhl, loc. cit., suggests a threefold basis of location for the purpose of 
a general theory of location : rent, other local cost as a whole, and transporta- 
tion cost. But if rent is, as I think was shown sufficiently, a function of location, 
it is theoretically quite unsatisfactory to assume it as a general or direct "fac- 
tor" of location. This aspect of Predöhl's arguments was also questioned by O. 
Engländer (although from another viewpoint), "Kritisches und Positives zu 
einer allgemeinen reinen Lehre vom Standort," Zeitschrift für Volkswirtschaft 
und Sozialpolitik, Vol. V, Nos. 7-9 (1926), and Predöhl's reply, "Zur Frage einer 
allgemeinen Standortstheorie," Zeitschrift für Volkswirtschaft und Sozialpolitik, 
Vol. V, Nos. 10-12 (1927). 

" Cf ., for example, J. M. Clark, Economics of Overhead Costs, particu- 
larly pp. 82-83. 

^^ I do not know hov/ much weight can be attached to Russian statistics in 
matters of this kind, but if the recent census is fairly correct, the development 
in Soviet Russia seems to be at least in accordance with this statement. Cf. For- 
eign Affairs, VI, 333, In this connection it is amusing to note that Weber's theory 
of location has been translated into Russian in recent years and acquired a great 
vogue in that country, I am told. The independence of its conclusions from the 
price mechanism lends it significance there, perhaps. 


since rent would be an element of the cost of production in a so- 
cialist state, such an acceleration would be impossible in the long 
run, and that the final equilibrium would be identical. However, 
what has been said about the locational foundation of rent, sug- 
gests a more complex situation, as we are apparently dealing 
with interdependent variables. 

In applying the theory of location to the theory of transport 
rates, a suggestive start has been made by Oskar Engländer. A 
good deal of light is shed also upon this aspect by Stuart R. Dag- 

Finally international trade was taken up by Alfred Weber 
himself.*^ In his general work he attacked the theory of the 'in- 
ternational division of labor," thus taking a stand opposed to 
that of many other economists.*^ The forces which seem to de- 
termine the location of industries would obviously permeate the 
international field, and this led Weber to apply the rules which he 
had found to the problems of international trade. One might 
start from the assumption of an even distribution of the different 
kinds of production over the entire earth rather than from the 
assumption of the ''international division of labor." The classical 
doctrine of free trade, says Weber, takes only capital and labor 

*® Cf . his The Principles of Inland Transportation and Oskar Engländer, 
Theorie des Güterverkehrs und der Frachtsätze. 

*~' "Die Standortslehre und die Handelspolitik," Archiv fuer Sozialivissen- 
schajt und Sozialpolitik, XXXII (1911), 667 ff. There is some hope that this 
whole aspect of the theory of location will be further developed soon. Bertil Oh- 
hn has recently ventured upon the bold assertion that "the theory of interna- 
tional trade is nothing but an international theory of location" ("1st eine Mod- 
ernisierung der Aussenhandelstheorie erforderhch?" Weltwirtschaftliches Archiv, 
XXVI, 97 ff.). It does not become very clear from this article, unfortunately, 
how Ohlin expects to elaborate upon his theme. 

** Cf., for example, A. B. Clark (in Palgrave's Dictionnry, 1923) : "By local- 
ization of industry is meant the concentration of different industries in different 
localities, a phenomenon in its international aspects aptly described by Torren's 
phrase 'territorial division of labor.' " This in 1923 ; the article [on localization] 
does not even mention the Standort der Industrien." 


into consideration when discussing costs of production, while the 
''natural" factors are supposedly eliminated by the Ricardian 
theory of rent. This approach makes it impossible to appreciate 
the independent significance of the costs of transportation. The 
picture of the "natural" tendencies of the distribution of eco- 
nomic forces shows really four stages (or layers) : 

1. The farming population will be distributed rather evenly 
around the historical centers of culture and population (Thii- 
nen's belts). 

2. All industries which remain so oriented under the influ- 
ence of costs of transportation (i.e., industries which use more 
"pure" materials or ubiquities than weight-losing materials) will 
be evenly distributed upon this foundation. 

3 . Industries which show considerable weight losses during 
the process of production will be attracted to the deposits of raw 
materials and fuels. 

4. Industries with high labor costs per ton of products will 
be concentrated at the favorable international labor markets. 

From this it will appear that the classical doctrine (proba- 
bly upon the basis of actual events in England at the time) con- 
centrated its attention upon the fourth stage and attributed to it 
a good deal of what was probably due to the third. However, 
there is a certain recognition of Weber's point of view (al- 
though, as we have shown, without the theoretical foundation) 
in Marshall.*^ Friedrich List, in a sense, represents a reaction 

^Principles, 4 ed., p. 761. "It is no slight gain that she [England] can make 
cheaply clothes and furniture and other commodities for her own use ; but those 
improvements in the arts of manufacture which she has shared with other na- 
tions have not directly increased the amount of raw produce which she can ob- 
tain from other countries with the product of a given quantity of her own cap- 
ital and labor. Probably more than three-fourths of the whole benefit she has 
derived from the progress of manufactures during the present century has been 
through its indirect influence on lowering the transport of men and goods, of 
water and light, of electricity and news; for the dominant economic fact of our 
own age is the development, not of the manufacturing, but of the transport 


against the classical overemphasis upon labor costs when he says 
that wherever there is agriculture there must also be industry. 
But he does not undertake to construct a theoretical foundation 
for this aspect of his protest. Only upon the basis of an adequate 
theory of location is it possible to fit the two points of view into a 
satisfactory theoretical harmony. 

It seemed primarily desirable to point out the significance 
of isolating costs of transportation for any theory of location. In 
spite of the apparent distortions which the network of locations 
as determined by transportation costs alone is subject to in the 
international field, a clear analysis of the working of this fac- 
tor has much to contribute toward a deeper understanding of the 
forces underlying the international distribution of industries."^ 
Weber's new approach enables him to restate the doctrine of free 
trade. If the natural evolution tends to develop new industrial 
centers, such tendencies may be retarded or accelerated, but 
they cannot be eliminated. 

To summarize, land rents, i.e., advantages due to favorable 

industries. It is these that are growing most rapidly in aggregate volume and 
individual power, .... they also which have done by far the most toward in- 
creasing England's wealth." (ItaHcs mine.) But why? If the costs of transpor- 
tation are so important, their operation ought to be given the appropriate at- 
tention. That this whole matter is in some way related to the question of land 
value and rent is also asserted by Marshall : "The influence on values which has 
been exerted in the modern age by the means of transport is nowhere so con- 
spicuous as in the history of land; its value rises with every improvement in its 
communications with markets in which its produce can be sold, and its value 

falls with every new access to its own markets " 

*°Says Weber (Archiv, loc. cit., p. 668): "Jede äussere Handelspolitik be- 
deutet, wenn sie einen bewussten, willkürlichen Eingriff in das natural Gegebene 
darstellt, den Versuch, Produktionszweige in einen Wirtschaftskörper hinein und 
aus anderen herauszuziehen, sie in ihrer geographischen Lagerung zu beeinflussen, 
zu verschieben." This aspect has recently been expanded upon and has been made 
the basis of historical systematization of the problem of the interrelation between 
locational development and the growth of the modern state by Hans Ritschl, 
"Reine und historische Dynamik des Standorts der Erzeugungszweige" in Schmol- 
lers Jahrbuch, Vol. 51, pp. 813 ff. 


locations of industry in relation to raw material deposits and 
market areas, appear to be variable functions of the locations of 
industry which are in turn variable functions of dynamic (or 
creative) factors, such as the development of new material re- 
sources, transportation facilities, or increases in population which 
determine economic development in the long run. An adequate 
theory of location seems bound to enrich the theory of land rent 
and thereby perhaps carry repercussions into other aspects of 
the theory of value. 

Carl Joachim Friedrich 


The question of the location of industries^ is a part of the 
general problem of the local distribution of economic activities. 
In each economic organization and in each stage of technical 
and economic evolution there must be a "somewhere" as well as 
a "somehow" of production, distribution, and consumption. It 
may be supposed that rules exist for the one as well as for the 
other. Still, political economy, in so far as it goes beyond the 
analysis of elemental facts and beyond pure theory, is of neces- 
sity primarily description and theory of the nature of economic 
organization (Wirtschaftsart J. The presentation and theoreti- 
cal analysis of the nature, the sequence, and the juxtaposition of 
the different kinds of economic organization is its natural con- 
tent as soon as it attacks concrete reality. This is such an enor- 
mous content that it should not occasion wonder if a young sci- 
ence, limiting itself in its initial tasks, treats the "somewhere" 
of economic processes simply as a function of the nature of that 
process, although the location of an economic process is only 
partly a function of its nature. In other words, political econo- 
mists have dismissed this problem of location with some general 
references to rules of local and international division of labor, 
etc., or political economy has left to economic geography the 
theoretical consideration of the distribution of economic proc- 
esses over a given area. Naturally, the latter is able to approach 
the problem only in so far as it can be explained by purely phys- 
ical facts. The result is as unsatisfactory as if we had left the 
analysis of the nature of economic processes, i.e., political econ- 
omy, to the technical sciences. 

But while problems of location have been treated by geogra- 

* Industries is here and throughout the text used in the sense of manufactur- 
ing industries. — Editor. 


phers primarily, Thünen is a notable exception. There are, too, 
several later attempts in this field. But they are insignificant 
when compared with the magnitude of the problem. We witness 
today enormous displacements of economic forces, migrations of 
capital and human labor such as no other age has ever seen. We 
see "empires rise, empires fall," apparently as the consequence 
of such locational changes. We follow these developments with 
a strong feeling of their significance; we predict the tendencies 
of future accumulation and distribution, the development of in- 
dustrial states and their collapse. We even interfere with these 
matters by our trade and tariff policies (Handelspolitik), and 
try to master them. In short, we do repeatedly a thousand things 
which we should really attempt only after we have secured a 
clear understanding of the laws which operate within this sphere. 
But can we say that we possess such a knowledge? Can we say 
that in our discussions we make use of much more than some 
vague notions about the division of labor, etc., while assuming 
location to be determined by the nature of the particular proc- 
ess? We work, in spite of Thünen and his successors, almost 
entirely with such tools, I believe. 

We also notice enormous displacements taking place within 
national boundaries. We observe that certain regions rapidly 
grow poor in human beings and capital, while others become sat- 
urated. We see in metropolitan centers great masses conglom- 
erate, seemingly without end. We philosophize about these mat- 
ters, talk about the advantages and disadvantages which result, 
about Asphaltkultur, or ''decline of morals." Of course we have 
long since become partisan in these matters. To some of us it 
seems that the populace "runs" to the big cities only for "pleas- 
ure's" sake — to the ultimate ruin of itself and its posterity; to 
others it appears that these people follow inevitable laws, as for 
example the flow toward the place of lowest pressure socially, 
etc. Much thought has been spent upon the "rush to the city" 
(not only upon its consequences, but also upon its causes), but 


is it possible for us to arrive at any conclusion about its causes 
when we do not possess as yet any real knowledge of the general 
rules determining the location of economic processes — ^when the 
purely economic laws which without any doubt somehow influ- 
ence location are not discovered? 

Everybody who moves into a large city goes there, among 
other purposes, in order to follow some economic pursuit. Is it 
sensible for us to argue about cultural and social motives when 
perchance we are simply fettered by the iron chains of hard eco- 
nomic forces? It may be that the enormous agglomerations of 
today are nothing but inevitable results of a certain stage of eco- 
nomic and technical development; or perhaps they are the con- 
sequence of the social organization of our economic system. 
Concerning this we really ought to have some exact knowledge. 
At any rate we cannot very well go ahead assuming that there are 
no rules of economic location at all, or that people are guided by 
"pleasure" and other irrational motives when choosing the loca- 
tion of their economic pursuits, although we know them to be 
controlled by hard-and-fast rules in every other economic sit- 

Ambition might tempt us to formulate a general theory of lo- 
cation. For it seems possible only on the basis of general rules 
of locational distribution of economic forces to disclose the caus- 
al relation between them and those large displacing processes 
which we observe. With such general rules known, it would be 
possible to show how and to what extent the aggregation of pop- 
ulation is determined by economic forces. Having acquired this 
knowledge, we might become able to say how far forces of a 
general cultural nature determine the location of economic proc- 

But certain reasons make it advisable to limit our inquiry to 
a theory of industrial location, reasons quite apart from such en- 
tirely personal facts as the time and strength of an individual. 

For one thing, the theory dealing with the nature of eco- 


nomic processes has, with much profit, separated the spheres of 
production, distribution, and consumption. We gradually gain 
the basis for a general understanding of the economic system by 
learning how the phenomena of different spheres are interre- 

Still, as a matter of fact, the locational forces operating be- 
tween the different spheres are quite peculiar. We may separate 
production, distribution, and consumption as far as we please, 
but, analyzing the locational character of an economic system 
(Wirtschaft), we need to explain a large part of each of these at 
the same time. For example, the locational distribution of con- 
sumption appears to be, with slight exceptions, nothing but lo- 
cational distribution within the other two spheres, seen from a 
different point of view. Only the relatively inconsiderable num- 
ber of people who are, economically speaking, merely consum- 
ers, such as officials, soldiers, and persons of private means, 
move about independently of the other two spheres. For the 
rest, each producer, laborer, merchant, or the like, wherever he 
may be, affects to some extent the location of consumption. In 
turn, each consumer, wherever he may be, affects to some extent 
the locational distribution within the other two spheres. 

The limitation assigned to our study is, therefore, in fact, to 
a large extent a matter of appearance only. That part of dis- 
tribution which represents the actual movement of goods is ge- 
ographically imbedded either between the different parts of 
production (productive process of distribution) or between pro- 
duction and consumption (consumptive process of distribution). 
It is impossible to explain the sphere of production locationally 
without including in this explanation the distribution of mate- 
rial goods in all its aspects. In the theory dealing with the nature 
of economic processes it may be possible to have production end 
at the point where the product is sold to a merchant, at least 
abstractly; but for the purpose of explaining the economic loca- 
tion of production this procedure is impossible. Each part of 


production orients itself geographically with consumption in 
mind. The explanation of this orientation — locational theory — 
cannot neglect consideration of the place of consumption. Thus 
in fact we include the distribution of goods in our theory. 

Because of this inevitable interaction our theory does not, 
however, become a complete theory of the location of distribu- 
tion. We in no way explain thereby the location of the seats of 
the wholesale merchants, of the agents who direct the actual 
movement of goods, i.e., the location of the trading centers. The 
headquarters directing the circulation of the goods and this cir- 
culating process itself must be disconnected geographically. 

Moreover, we say nothing definite regarding obligations and 
money, that is, we say nothing definite concerning the location 
of the centers of capital and credit. This being true, some as- 
pects of the collateral spheres of the economic system remain 
unexplained. These collateral spheres must be treated separate- 
ly when one method is that of isolating" the various factors. 
And, for that matter, these collateral spheres have a geographi- 
cal movement of their own, and their location should according- 
ly be explained separately. 

As has been indicated, if we take the sphere of production 
and explain its location completely, we shall of necessity explain 
also the larger part of all other locational problems within the 
economic organism. Practically speaking, we approach the total 
problem of economic location from one particular point; the 
first steps will be a theory of the location of production, but the 
last ones will be essentially a general theory of location — or at 
least it will not be very difficult to arrive at such a theory. 

Limiting ourselves thus to the sphere of production, it is of 
prime importance to seek an explanation of the location of in- 
dustrial production. There are good reasons why we should con- 
tent ourselves with this analysis. We have a theory of the loca- 
tion of agricultural production by Thiinen, although it needs, I 

^ This isolating process, it is true, is largely formal and abstract. 


believe, some reshaping, and particularly some developing. But 
we do not as yet have any theory of the location of industries — 
we may say that without doing injustice to the work of Roscher 
and Schaeffle — although it is obvious that industrial location is 
far more important for explaining the large modem displacing 
processes. To be sure, very nice and interesting facts determine 
the locational displacements of the different methods of agricul- 
tural production. But they are upon the whole simple, extensive- 
ly analyzed, well-known matters, at least to the extent to which 
they go beyond technical details and influence international eco- 
nomic displacements and the modern aggregations of population. 
Moreover, they have in a certain sense created only the basis of 
the general locational revolution of recent times; they have pro- 
vided merely the groundwork upon which other forces have 
arisen to displace economic processes and to determine the ag- 
glomerations of population. This we sense quite distinctly as 
the modern "enigma" which is to be solved. Mysteries are not 
contained in the agricultural sphere. If they can be found any- 
where in economic matters, and especially if they can be found 
in the sphere of production, they will have to be discovered in 
the industrial sphere and in the locational rules which control it. 
The locations of the industries form the "substance" (I do not 
say the cause) of the large agglomerations of people today. We 
view their movements quite superficially, and with perhaps too 
few misgivings as to the international implications of the shift- 
ing of forces. We argue seriously about tendencies in this sphere. 
It is highly important, therefore, to begin by clarifying these 
tendencies, not only because they are greatly neglected, but also 
because they are most far reaching in fact. 

How shall that be done? 

It is well worth noticing that we know the simple facts about 
the distribution of agriculture better than those about the dis- 
tribution of industry. This situation is quite easily explained by 
the greater complexity of the industrial sphere. We have well- 


developed statistics which cover fairly well the areas of cultiva- 
tion of the different agricultural products, the size of the crops, 
and their international as well as their local distribution, the lat- 
ter at least in many countries. We have data, and we can even 
say that on the whole the data are scientifically analyzed. The 
essential aspects of agricultural locational distribution and de- 
velopment are known to us; if not, it is our own fault. 

With regard to industries, however, we are confronted at the 
very outset with gigantic difficulties in getting the mere mate- 
rial.^ We do not even know the raw figures of international dis- 
tribution of production of more than a few trades, such as mines, 
salt works, sugar, tobacco, and perhaps the mechanical part of 
the textile industry — in other words, trades whose production is 
analyzed statistically for fiscal or other special purposes. For all 
other industries we use, for want of better data, the import and 
export figures in a manner scientifically quite inadmissible. 
When we talk of international distribution of industrial resources 
we use figures which we should not use at all except in terms of 
their relation to the size of the original production. The trade 
censuses which, by giving the number of persons employed, give 
us suggestions regarding size, are very difficult to compare, and 
for that reason are not thus used. This is the situation regarding 
the distribution of industries internationally. 

What is to be said concerning the distribution within the na- 
tional boundaries? Material exists regarding this, although part- 
ly hidden so far. Here the trade censuses, or at least their pre- 
liminary and intermediary materials, can give us information 
about local displacements of a very exact kind and free from all 
objection. We do not do injustice to anyone by saying that this 
really extensive material has so far not been analyzed for these 
purposes. The geographical conditions of distribution and local 

^ This was written in iqog. But even today many of the essential facts are 
not available. — Editor. 


accumulation have nowhere as yet been analyzed in a careful 
quantitative way for even one industry. Of what use for our 
purposes are beautiful maps showing us the regions within which 
one industry is practiced "primarily" if we learn that this same 
industry is also practiced ''outside" of these regions within the 
same country?* We ought to know, for purposes of any exact 
locational study, to what extent they are practiced "inside" and 
"outside," i.e., the relation, quantitatively speaking, between 
the two. Similarly useless for our purpose are otherwise quite 
estimable maps which show us the "relative geographical im- 
portance" of various industries in relation to the population;^ 
they give us information concerning the different composition of 
the population here and there, but not concerning the geograph- 
ical distribution of the industry itself. If we search for quanti- 
tatively well defined information regarding the local distribution 
of industries, we soon find that we grope in the dark concerning 
all industries in all countries, with perhaps the single exception of 
mining and smelting production. We grope in the dark concern- 
ing every single period of the development of a given industry 
— and how much more so concerning its entire development! 
My respects, therefore, to economic treatises including any dis- 
9 cussion of local distribution of industry at present! Nothing is 
to be said against them as things stand. We ought to realize, 
however, that they are in fact little more than rather sketchy 

Obviously a change should be brought about in this situa- 
tion. It is necessary to canvass systematically the existing ma- 

* Compare the maps of numerous writings on the English industries ; simi- 
larly, the maps of distribution of industries which are added to the reports of 
factory inspection. 

^ Compare the maps of the official German reports on the Trade Census. 
They are used and even elaborated for the purpose of illustrating the location of 
industry in Teubner's Handbuch der Wirtschaftskunde Deutschlands, I suppose 
faute de mieux. For evidence that they are not only useless in principle, but that 
one gets quite a distorted idea about the whole matter, compare Part II. 


terial available upon one period, and we shall choose the German 
development since i860 for that purpose. It is further neces- 
sary to get a rehable picture by making an exact quantitative 
analysis of the interrelated forces which affect the distribution 
and agglomeration of the individual industries. This is the first 
and unavoidable part of our investigation, to get exact data re- 
garding the actual locational relations and displacements in any 
one tolerably isolatable district for some period of time, even if 
quite limited. We need to have before us the object with which 
we are dealing, clear and discernible, and particularly measura- 
ble, in all its parts. 

But we want still more, and we must attempt more, as has 
been indicated earlier. We want to discover "laws" for the move- 
ments within this (industrial) body — laws sufficiently exact to 
enable us to measure, with their help, the displacement of eco- 
nomic forces in such a way that we can state to what extent these 
displacements, and to what extent other factors cause the vast 
geographical revolutions of our time. 

The empiricist will at best look askance at this larger and 
more essential enterprise. He will in his well-known fashion tell 
us that we should have to be able to subject the social life and 
its forces to experiments if we wish to find exact, i.e., scientific, 
laws ; ^ that inasmuch as we cannot do that, we ought to content 
ourselves with stating ''probabilities" and more or less certain 
''relationships," "regularities," "phenomena of evolution." Any- 
thing else is useless from his point of view, and we cannot, there- 
fore, expect sympathy from that side. But we may hope for 
sympathy among those who believe with us that it is possible 
without experiments to analyze further by purely theoretical, in- 
tensive labor empirical evolutionary phenomena, in spite of their 
complexity. By making use of the method of isolating analysis, 

® Scientific stands here for the German term naturwissenschaftlich, as op- 
posed to geisteswissenschaftlich. The distinction roughly corresponds to "scien- 
tific" and "philosophic." Cf. Rickert, Kulturwissenschaft und Naturwissenschaft, 
4th ed., 1 92 1. — Editor. 


we may ascertain, if not all, at least some, causal relationships, 
and prepare for a perfect causal understanding, and even for 
measurement. By the adherents of the method of isolation, then, 
this essay, whether successful or not, will probably be approved, 
10 at least in principle. We hope that the writer, and not the es- 
say, will be blamed for its possible failure. 

This will make clear how we must proceed with this essay. 
Obviously, two different purposes should be achieved. First, we 
shall have to develop the pure laws of industrial location, laws 
in the strictest sense of the term pure, i.e., independent of any 
particular kind of economic system (Wirtschaftsart) J Second- 
ly, we shall have to show what particular form these laws re- 
ceive in the modern economic order, and what additional rules, 
or perhaps only regularities, enter. The second phase of the 
work will of course contain an explanation of the interesting re- 
lationship^ between these two kinds of laws and the large social 
revolutions referred to. 

Methodologically we shall always proceed by isolation, not 

'' The concept of a system of "pure" economics as indicated here occurs in 
German theoretical literature. It is the outcome of an attempt to regain for eco- 
nomic theory a position which it seemed to have lost completely under the im- 
pact of the historical school. Books like Karl Biicher's Introduction to Polit- 
ical Economy treated economics in terms of economic development. Usually 
several stages were being distinguished, of which the last is the capitalistic stage, 
or lately the high capitalistic (hochkapitalistische Stufe). In order to get a foot- 
hold outside this evolutionary view and to return to theory, the expedient of 
such an abstract "pure" system was used. It seemed sensible to say that if all 
these systems were designated as economic systems, it was justifiable to search for 
the characteristics which they had in common, although some will hold that the 
thought of the earlier thinkers like Smith and those following him is "capital- 
istic" and representative of the stage of development with which they were con- 
cerned. The assumption of such a "pure" system of economics simply marks the 
return to what would be styled "economic theory" in England and America. Cf. 
also infra, p. 226, footnote. — Editor. 

* Relationship is here used for Dynamik, a German word which is not al- 
ways suited for translation into the English "dynamics," and which therefore has 
occasionally been rendered by "forces" and "relationship," respectively, depend- 
ing upon the particular meaning it has in the respective connections. — Editor. 


only in the first part dealing with the pure theory, but in the 
second part^ as well. There is one difference, however. For the 
task of stating the pure rules of location it will be possible to use 
deduction exclusively. We shall be able to start from certain 
very simple premises and to deduce therefrom the entire system 
(Mechanik) of "pure" rules of location. Naturally, this system 
will apply only in terms of these premises and no further. It 
will become apparent that it is possible to develop these pure 
rules of location fully in so far as they are of a general nature, 
and apply therefore more or less to all industries. For the details 
compare chapter i. 

The further task of formulating the laws of location under 
modern capitalism cannot be achieved by simple deduction. The 
premises which determine the particular application of the pure 1 1 
rules as well as the additional rules governing reality are not 
known without further investigation. In order to formulate them 
we must first secure the actual picture of industrial orientation 
(location), as it is moulded by the modern economic life. Once 
we have this actual picture we shall have to show to what extent 
this orientation is affected by unexplained speciaP^ causes which 
the general theory has ignored and may properly ignore.^^ Fi- 
nally, we shall have to show the effects of unexplained causes of 
a general kind. For these latter we shall have to find the prem- 
ises which must somehow be due to the particular nature of 
modern economic or social life. Only from these premises may 
we deduce the rules of location "governing reality," which can 
give us a complete picture of the distribution of locations and at 
the same time can perhaps give us the means of understanding 
the general aggregations of population in modern times — that is, 

^ An outline of this second part is contained in Alfred Weber, "Industrielle 
Standortslehre (Allgemeine und kapitalistische Theory des Standorts)" in Grund- 
riss der Sozialökonomik (1914), Abteilung VI, i, 70-82. — Editor. 

'^^ Due to circumstances in particular industries. — Editor. 

" Details in chap. i. 


so far as such a thing can be done by an abstract theory, which 
never explains entirely a concrete reality. 

Obviously then, the preliminary canvass of facts which I 
mentioned earlier is a necessary introduction to the later task of 
a '^reahstic" theory. I had, in fact, undertaken this preliminary 
work of ascertaining precisely the evolution of German indus- 
trial location since i860 before I had acquired any theoretical 
conception. I beheve, however, that it will be better to present 
this factual material where it belongs, both as a matter of logic 
and as a matter of practical presentation : after the pure theory 
and before the realistic theory. It is impossible to analyze or ar- 
range this material at all without an abstract theory of location. 
I have indeed gained it myself from this analysis; only out of an 
abstract theory and a clear survey of the facts can the realistic 
theory be compounded.^^ 

We shall organize this work, then, as follows : The first part 
will contain the pure theory. This is divided into two parts: (a) 
the abstract disclosure of the economic forces which control the 
12 orientation of industries, i.e., the analysis of the constituent ele- 
ments (locational factors) determining the location of industries, 
and (b) the formulation of the laws according to which these 
factors work. 

The second part will contain the ''realistic" theory and will 
be based upon: 

a) An analysis of the locational distribution (Lagerung) of 
German industries since i860. 

b) An analysis of some other data which are available con- 
cerning the aggregation of population in modern capitalistic 

We shall see that the kind of industrial location which we 
have today is not entirely explained by the "pure" rules of loca- 

" It has to be kept in mind that Professor Weber does not work out his so- 
called "realistic" theory in this volume. An approach to it is made in his con- 
tribution to the Grundriss der Sozialökonomik. — Editor. 


tion, and therefore is not purely "economic." It results to a large 
extent rather from very definite central aspects of modern cap- 
italism and is a function of modern capitalism which might dis- 
appear with it. It results, we may say in hinting at the main 
point, from degrading labor to a commodity bought today and 
sold tomorrow, and from the ensuing laws determining the labor 
market {Gesetze der " Arbeitsmarktgestaltung^') and from the 
local "agglomeration of workers" created thereby. This agglom- 
eration of workers produces by necessity the particular kind of 
industrial aggregations which we find today and which I shall 
call "progressive agglomeration of industry" {Stufenagglomera- 
tion der Industrie) . Therefrom results, as we shall have to show, 
the phenomenon of modern aggregations of population and, of 
course, many other things. 

I say this only to indicate that the "realistic" theory will en- 
able us to arrive at certain fairly general conclusions which 
explain at least a part of the dynamics of the large modern geo- 
graphical revolution. But only a part; the limit of the conclu- 
sions of the second section of our study will be found in the limits 
of its material. This material deals mainly with the movements 
of industry within only a part of the international economic or- 
ganism — within a territory which represents a politically, and, 
generally speaking, a nationally uniform organization. This lim- 
itation in the material has the advantage that the movements 
of industry thus studied present themselves to the observer as, in 
a sense, "pure." They take place without regard, on the one 13 
hand, to any differences of political organization and to the in- 
fluence of trade and tariff policies; and without regard, on the 
other hand, to differences of race, climate, and environment. Our 
studies thus provide without doubt an analysis for one country, 
and apparently they provide the first necessary step toward a 
similar theory for the Weltwirtschaft (economic system of the 
world) ; for a general theory would, at the outset, also disregard 
the constituent differential elements just mentioned and would 


introduce them afterward/^ The limitation in the material has, 
however, a disadvantage in that it does not help us to ascertain 
precisely the significance of each of the differentiating factors 
mentioned above. In this respect the limitations of the material 
set a limit to everything attempted in this essay, a fact which 
cannot be emphasized strongly enough. 

This is, of course, the point at which further study is desir- 
able. It should be said, however, that further research becomes 
rather difficult. We need, in order to get ahead, rather diversi- 
fied new data. We need primarily clarity as to ideas and facts 
concerning the general significance of such fundamental factors 
as national disposition (Volksanlage) and environment — both 
their general significance and their relationship to what we call 
labor supply (Arbeiterstamm). We need to ascertain precisely 
how far the quality in its different parts of industrial output de- 
pends upon the "stock of industrial workers" in different cli- 
mates (Zonen) and among different nations, and how far this 
dependence changes within the framework of the modern tech- 
14 nical and economic development, etc.^* For an understanding of 
the international problem we need, moreover, investigations into 
the actual effects of political interferences (such as trade poHcies 
and labor policies) upon the local grouping of economic forces-^ 
studies which we do not possess at present in spite of all our the- 
orizing regarding international trade and tariff policies. We 

^" There is no question that the importance of some of these differentiating 
factors (particularly the trade and tariff policy) is generally very much over- 
estimated today. But there is no question, either, that others, like climate and 
cultural environment, perhaps even "race," have considerable importance — so 
considerable, in fact, that they will be felt even in analyzing the seemingly uni- 
form German body, and that some "dark spots" which remain can hardly be ex- 
plained except by them. The available statistical material unfortunately does not 
allow to solve these problems. 

'* Cf . in this connection the researches of American sociologists, i.e., Clark 
Wissler, Man and Culture, F. Stuart Chapin, Cultural Changes, and P. Sorokin. 
Social Mobility. — Editor. 


should also secure an enormous mass of material concerning the 
international distribution of industrial location {internationale 
Industrielagerung), etc. These are many and difficult matters. 

But irrespective of this, we shall of course find that much of 
what is presented within the narrow frame of this essay must be 
corrected, and the reader will observe that there remain unsolved 
problems, a fact which will not be concealed. 

This book is expected to be a beginning, not an end. 15 



The economic causes determining the location of an industry 
seem to be a network of complex, diverse elements, often in in- 
dividual instances so arbitrarily, or at least incidentally, com- 
posed that there appears to be no place for more than an analysis 
of the individual case/ It seems impossible to make any general 
statement for most industries concerning the places to which 
their factories must go or concerning the causes upon which 
their locations depend. If we approach the individual manu- 
facturer with a question concerning the choice of his location, he 
will at most give us a quaint concoction of general and particular 
reasons, unless he points to the past and says: ''I am here be- 
cause this industry grew up here." This concoction will be dif- 
ferent for each factory and will present whatever general causes 
it contains in a particular individual setting. Thus one might 
well despair, as I have said, of discovering general formulas for 
the solution of the different elements, or even of ascertaining pre- 
cisely their limits. Still, an attempt to do so is quite necessary 
from a theoretical point of view. However difficult it seems, we 
must try to disentangle the knot of causes which confronts us 
everywhere in reality, and to isolate and group the elements com- 
posing it. 


In order to do this we need a clear understanding of two 
terms: first, the forces which operate as economic causes of lo- 

' Cf. R. M. Haig, "Some Aspects of the Regional Plan of New York and Its 
Environs," and "Toward an Understanding of the Metropolis," Quarterly Jour- 
nal of Economics, Vol. XL. — Editor. 



1 6 cation, the ''locational factors"; and second, the objects which 
we believe those causes to act upon, the ''locational units." 

By "locational factor" we mean an advantage which is 
gained when an economic activity takes place at a particular 
point or at several such points rather than elsewhere. An ad- 
vantage is a saving of cost, i.e., a possibility for the industry to 
produce at this point a certain product at less cost than else- 
where, to accomplish the entire productive and distributive proc- 
ess of a certain industrial product cheaper at one place than at 

We say the productive and distributive process of a certain 
product. We shall always compare for one and the same product 
the advantages of production as represented by locational fac- 
tors; since only the production of one and the same product 
constitutes a unit with regard to the spatial distribution of which 
we may speak with sufficient accuracy. 

It is necessary to be exact in this respect: a given com- 
modity of better quality is not the same product as the same 
commodity of inferior quality, at least not in principle. The pro- 
duction of each is, from a theoretical point of view, a "unit" in 
itself which is distributed over an area according to its pecu- 
liarities. These units can and do compete with each other; the 
better commodity may supplant the less good, or vice versa, and 
this may also affect their locations eventually. But this competi- 
tion or displacement is not essentially a locational struggle ; it is 
based upon competitive causes of a different kind. It does not 
concern us for the moment. It represents the displacement of 
one industry by another, in the same way in which wood and clay 
products are superseded by iron goods. It is, however, an object 
of our study to learn whither the victorious or the defeated in- 
dustry and the production of the different qualities move. We 
have to solve that problem by analyzing the local distribution of 
the productive advantages which are decisive for this particular 

17 quality, this "locational unit." 


It is obvious that, practically speaking, it may and fre- 
quently will be the case that the extent and the importance of 
a given productive advantage is negligible as between different 
j qualities of the same product. It may happen that for different 
qualities of a product the locational factors are so similar that 
they are, practically speaking, equal. But even so, these different 
qualities represent independent units for the purpose of loca- 
tional analysis. It must be kept in mind that each of the qualities 
has its particular sphere of consumption, competing, perhaps, 
but separate. It is consequently not possible to treat the produc- 
tions of these different qualities as one locational unit, even 
I though they are in close proximity (have deposits of raw ma- 
i terials and other real locational elements in common). We have 
i to deal with two different productions which happen to find their 
locations according to similar causes. 

The foregoing, however, is the abstract position of pure the- 
ory. As a matter of fact, there is in reality an enormously wide 
field in which the competition of quality changes to that of price, 
and in which products of a different but closely approximate 
quality are in fact treated as one and the same product at dif- 
ferent prices. Viewing the matter closely, one is compelled to 
admit that each "competition of price" rests partly upon such a 
difference in quality; because the quality of no product is truly 
equal to that of any other. Competition of price is possible only 
by disregarding differences of quality. 

Still, whenever in reality no difference of quality is recog- 
nized, we do not need to recognize it when applying theory to 
reality. In such a case we have before us, for this one application 
at least, "units" of location of production. The different qualities 
of product have been welded together into a unit by life through 18 
being treated as one by consumption. Accordingly, we shall 
treat as locational units varied products whose distribution of 
production over an area is properly to be analyzed as a unit. 


This much regarding the nature of the terms, locational fac- 
tors and locational units. 


How shall we group these locational factors? We seek a 
general theory of location; that is to say, we wish to resolve the 
seeming chaos of the local distribution of production into the- 
oretically general rules. Such general rules would result only 
from the operation of locational factors of a general nature, if at 
all. Such general locational factors must be considered for every 
industry, asking in the case of each industry in what way they 
exercise their general influence and to what extent. Thus the 
first question is: Are there such general causes of location which 
concern every industry? And the next question is: Are there 
any special causes of orientation which concern only this or that 
industry, or this or that group of industries? Such special causes 
obviously are the result of the peculiar technical or other nature 
of an industry or group of industries. How far can the location 
of industries be explained by general causes, and how far only by 
introducing special causes? It is obviously helpful to classify 
locational factors as general and special. It may elucidate the 
difference to state at this point that the cost of transportation, of 
labor, and rent are general factors, since they should be consid- 
ered in the case of every industry, influencing it ''more or less in 
19 one way or in another." On the other hand, the perishability of 
raw materials, the influence of the degree of humidity of the air 
upon the manufacturing process, the dependence upon fresh 
water, etc., are special locational factors, because they concern 
particular industries only. 

All locational factors, whether general or special, are to be 
further classified according to the influence which they exercise 
(i) into such as distribute the industries regionally and (2) into 
such as ''agglomerate" or "deglomerate" industries within the 
regional distribution. To "distribute regionally" means to direct 


industry toward places on the surface of the earth which are 
geographically determined and given, to draw industry to definite 
regions and thus to create a fundamental framework of indus- 
trial locations. To "agglomerate" and to ''deglomerate" means 
to contract industry at certain points within such a framework 
(irrespective of where the framework may be situated geograph- 
ically), and thus to determine the agglomerations which industry 
shows within the framework — something quite distinct from the 
process of regional distribution. 

If industry is influenced by the cost of transportation or by 
geographical differences in the cost of labor, industry is drawn to 
points geographically quite definite, though changing their posi- 
tion as industry develops. The factors which operate thus are 
regional factors of location. If industry, however, is brought to- 
gether at certain points by price reductions due to agglomeration 
itself, whether it be the more economical use of machinery or 
merely the advantage of being at a place where auxiliary trades 
are located; or if industry is driven from such congested places 
by the high rent; industry is agglomerated or spread within its 
geographical network according to certain general rules which 
are quite independent of geography. The factors which operate 
thus are agglomerative or deglomerative factors. 

A third distinction which ought to be made is that of natural 
and technical factors on the one hand and of social and cultural 
factors on the other hand. This distinction (also made in terms 20 
of the effects of the factors) cannot be fully made, however, for 
reasons to be considered shortly. It has the following meaning: 
The advantages which draw industries hither and thither may 
be given by nature. In that case they could be altered only by 
changes of these natural conditions, by the extent of the control 
of nature — in other words, by technical progress. They would 
be independent of the particular social and cultural circum- 
stances; at least there woud be no direct dependence. On the 
other hand, the advantages which draw industries hither and 


thither may be social or cultural phenomena, the consequence of 
particular economic or social conditions, or of a certain civili- 

For example, all differences in cost which result from the 
spatial position and climate of different places, particularly all 
differences of cost of transportation, are locational factors of the 
natural and technical kind, phenomena of nature which may 
only be altered by the technical evolution. The differences of the 
cost of some types of labor may be of the same nature (differ- 
ences in the hereditary qualities of the population), or they may 
be the result of a certain cultural environment (differences in 
the standard of living, or in acquired productivity of labor), and 
they are sometimes locational factors of a mixed kind. If a dif- 
ferent interest rate prevails at different locations of industry, 
that is something which bears no relation to any natural condi- 
tion, and represents a purely ''social" factor of location. 

It is desirable to make a clear distinction between natural 
and social locational factors. Under our method of procedure 
this distinction is bound to have considerable significance for us 
later. For it is apparent that every aspect of locational factors 
which is not of a natural or technical, but of a social, character 
cannot be an object of pure theory which is to be independent of 
particular economic or social conditions. Such aspects must be 
left to empirical theory. The importance of this classification of 
locational factors is indicated by the fact that it defines the two 
21 large subdivisions of our theoretical analysis. 

But it will prove its value later. For the present we shall at- 
tempt to build up the "pure" theory without applying the dis- 
tinction fully or exactly. To be specific, we shall exclude from 
the purview of the pure theory all locational factors of a purely 
social and cultural nature which our analysis of reality reveals. 
We shall not even investigate how far the natural and technical 
factors contain in their present form social and cultural elements 
which are due to the particular economic and social order, the 


particular civilization of today. In order to be exact we ought 
to make this investigation and then apply these social and cul- 
tural elements in the empirical or realistic theory. But this will 
not be done. It will appear that these elements do not alter fun- 
damentally the laws according to which they work; they merely 
determine in particular how these laws work out in reality. It 
is better to state at once these particular qualifications of the 
general rules, and to do so within the framework of the discus- 
sions of the pure theory, then to leave them to a special treat- 
ment. Accordingly, the analysis of the pure theory will, upon 
the basis of the natural and technical factors, be carried into the 
ramifications which the modern economic order presents. This 
method of treatment will enable us to reach the problem of 
reality at our first attempt, and at the same time to verify prin- 
ciples by reference to actual life. 2 2 

Our analysis will be based upon the distinction between gen- 
eral and special factors of location and upon the distinction be- 
tween regional and agglomerative factors. The distinction be- 
tween natural and social factors will only silently accompany 
our discussion. 


Can we survey the several individual locational factors 
which are to be found in the various industries? Obviously, a 
complete survey could be made only empirically. There is no 
method by which one could deduce from known premises the 
special locational factors which exist for given industries on ac- 
count of natural or technical peculiarities. But, after all, this is 
not what we need in order to group the chaos of facts conven- 
iently for analysis and theory. We need a knowledge of the gen- 
eral factors of location which are applicable to a greater or lesser 
degree in every industry. If we know these we are able to inquire 
how far the orientation of industries can be explained by them. 
Next, 1- y ascertaining further facts, we can investigate the par- 


ticular causes of phenomena not explained by the general fac- 
tors. These causes must spring from the specific characteristics 
of particular industries; they are particular locational factors 
which we do not recognize in advance, and can ascertain only by 
investigation. We shall attempt only the development of a the- 
ory which explains the working of the general factors. This 
theory can be developed after a survey of the general factors has 
provided its basis. 

We can further limit ourselves with respect to the locational 
factors needed as a basis for our pure theory by considering only 
general factors of the regional type. If we know these and their 
working, we can abstractly construe the geographical frame- 
23 work which is created by them (cf . above) . We can put in as one 
single force all the agglomerative and deglomerative factors and 
general causes of orientation not yet analyzed. They tend to 
create a certain number of agglomerations of a certain size — 
agglomerations which are not due to geographical influences. 
This single force may easily be imagined to be the resulting force 
which is invariably derived from the counteraction of agglomera- 
tive and deglomerative factors. We need only to analyze the 
importance and the working of this resulting force. The factors 
composing it we do not need to know.^ In short, the pure theory 
may be based solely on the knowledge of the general, regional 
factors of location which control industry. 

We have a simple method of ascertaining them. We can 
find all general factors of location controlling industry (with 
the exception of the agglomerative and deglomerative factors) 
by analyzing some isolated process of production and distribu- 
tion. These general factors must be at work in any such process, 
and may therefore be discovered by analyzing it. The agglomer- 
ative factors are excepted because they are at work between 
industries, and therefore cannot be found in an isolated process. 

^More regarding this point in the chapter on ''agglomeration," below. 


But we are not looking for them, an5rway; we are looking for the 24 
regional factors, and they may be found in the way indicated. 

We have to find, obviously, those elements of cost which 
differ according to the location of the productive process. If we 
can secure them, we have the regional factors of location of a 
general nature. "Locational factors" are, according to our defini- 
tion, "advantages in cost." They depend upon the place to which 
industry goes, and therefore pull industry hither and thither. 
This idea is decisive for our entire further procedure. 

Abstractly considered, an industrial process of production 
and distribution contains about the following steps or stages: 
(i) securing the place (real estate or ground site) of the location 
and the fixed capitaP for equipment; (2) securing the materials 
(raw and auxiliary materials as well as half -finished products), 
and the power and fuel materials, (coal, wood, etc.); (3) the 
manufacturing process itself; (4) the shipping of the goods. In 
each of these steps a certain expenditure of natural resources 
and labor is invested. In some cases this expenditure has already 
been taken care of to a greater or less degree, as in the case i or 

2 of fixed capital or half -finished products. In other cases, as in 

3 and 4, it falls entirely within the stage of production which is 
under observation. Each of these expenditures precipitates itself 25 
into the price (Warengeldpreis) which is secured for the product 

on the market. The expenditures of 3 and 4 are primarily labor 
costs; those of i and 2, primarily material costs. In analyzing 
the price of industrial products we meet again in the guise of 
monetary elements all those elements of cost which grow out of 
the expenditure of goods and labor in the productive process. 
We have to ascertain, first, which of these monetary elements 
(in so far as they are elements of cost) differ according to the 
location of the particular industry. These are the general re- 
gional factors of location. We have to discover, second, which 

^ For this use, cf . Palgrave, Dictionary of Political Economy, article on 
"Capital." — Editor. 


of them are expressions of a particular economic order {Wirt- 
schaftsform) and which are expressions of every economic sys- 
tem. The latter will be the general regional factors of industrial 
production, even though they appear in the forms of the modern 
capitahstic order. 

We shall have to base our theory upon these factors in their 
modem capitalistic form, which is the only one practically avail- 
able for analysis. Nevertheless we work with the elements of 
the abstract economic order {reine Wirtschaft) and accordingly 
formulate a cheory which applies to this abstract order also. 

The following remarks should be made concerning the fore- 
going analysis of the "natural" industrial process as transformed 
by the capitalistic economic order. All expenditures of labor and 
goods which constitute the process become monetary advance 
payments upon the future price of the product. By monetary 
advance payments we mean that the entrepreneur of each state 
of production makes advance payments in the form of wages 
and salaries to his employees, and in the form of prices paid for 
materials and machines to the entrepreneurs of the previous 
stage. The monetary outlays of a certain stage of production are 
nothing but the sum of all these advances which its entrepre- 
neurs must make. It should be remarked, however, that each 
26 stage adds two things to its advance payments: the interest on 
the capital it uses for these advances, and its "profit." In each 
successive stage these "additions" appear as increases of the 
cost of materials. Thus the monetary costs are advance pay- 
ments covering not only expenditure of goods and labor but also 
of interest and profit of the preliminary stages as well. These 
remarks may suffice to clarify the nature of the process which 
we are about to analyze. What form does this process take if 
observed in connection with the "natural organization" of a stage 
of production as shown previously? 

I. The first step in the natural process of production was 
the securing of the real estate for the location, and the securing 


of the fixed capital. This becomes cost of rent so far as the secur- 
ing of real estate is concerned, and cost of money [interest plus 
brokerage charges plus taxes — Ed.] so far as the securing of fixed 
capital is concerned. 

The real estate is not consumed; the fixed capital is con- 
sumed but gradually. Both appear in the final price of the prod- 
uct as the interest rate of the sums spent on them.* In addition, 
the fixed capital appears with a monetary rate of amortization 
proportionate to the time required to consume the fixed capital. 

2. The securing of the materials and power which consti- 
tutes the second step in the "natural" process of production is 
divided into the monetary cost^ at the place of their production 
and the cost of transporting them^ to the place of their consump- 
tion. We shall not analyze the costs of transportation for the 
present. The total price (Anschaffungspreis) paid for the ma- 
terials and power supplies plus the interest resulting from the 
advance of funds used for buying them enters the market price 
(Warenpreis) ; so do the costs of transportation. 

3. The third step, the process of transforming the materials, 
entails the consumption of the materials, the depreciation (Ab- 
nutzung) of fixed capital (Stehendes Kapital) and the utilization 
of human labor. The first two elements of cost have been con- 
sidered already. The last one enters into the market price (Wa- 

* It is, of course, of no significance whether this capital enters into the proc- 
ess as loans, so that the interest rate is stated by contract, or as the entrepre- 
neur's own capital. It must always be there, it is always consumed, and its in- 
terest rate must be provided for. The stipulated interest rate is, as is well known 
to theory, nothing but the expression of the interest on capital, becoming ap- 
parent under certain circumstances. Resting in principle upon Böhm-Bawerk, 
although in a somewhat more narrow sense, it is important for the analysis of 
cost as given here that I interpret this general interest on capital (Kapitalzins) 
as the price paid for goods enabUng one to overcome time (Zeitüberwindungs- 
güter). This advanced capital (Vorschusskapital), then, makes possible all the 
advance payments which compose the monetary costs as explained. 

° I.e., the price to be paid for them. — Editor. 

® I.e., the price to be paid for transporting them. — Editor. 


renpreis) as wages; but again, of course, plus the interest on the 
advance of funds involved. 

4. The fourth step, the shipping, is represented by the 
costs of transportation which further increase the price by their 
full amount plus the interest on the funds used. 

It should be noted here that in all these stages an additional 
element of cost exists which is called today general expenses, 
i.e., expenses of the general management, taxes, insurance, etc. 

If we group all these elements of cost according to their 
character and if we add as the last element of the price the profit 
of the entrepreneur, we get the following elements composing 
the price (Warenpreis): (i) Profit. (2) The interest rates of 
the fixed and operating capital {Anlage und Betriebskapital) of 
the different stages. (3) The rate of amortization of the fixed 
capital. (4) The cost of securing materials and power. (5) The 
wages. (6) The cost of transporting: {a) the (raw) materials 
28 and power, {b) the finished products. (7) The general expenses. 

Of these we can eliminate two, namely, i and 7, from fur- 
ther consideration. Let us take up first the general expenses ( 7) . 
To the extent that they are artificial enhancements of the ex- 
pense of production by political or other agencies (taxes, insur- 
ance), they do not belong in the field of ''pure" theory. To the 
extent that they are "natural" costs (general management, 
etc.), the local differences determined by geographical condi- 
tions which might make them regional factors of location are not 
sufficient to make them worthy of consideration in the general 

As for profits (i), they can never (at least not in the last 
stage of industrial production) become locational factors be- 
cause they are not elements of price, but its result. They can 
become an element of cost only by entering into the cost of ma- 
terials, etc., of succeeding stages as profits^ of earlier stages. As 

^It has often been observed that English poHtical economy has not sepa- 
rated profit from interest and wages of management. But Weber separates them 


such an element of cost they may become a locational factor for 
the later stages because it is conceivable that profits will vary 
from region to region and thus affect the ''natural" price of se- 
curing the materials (cf. Böhm-Bawerk). To give an illustra- 
tion: If a coal-trading association today fixes prices which vary 
from district to district and, not contenting itself with the same 
profits in all districts, collects higher profits in a "safe" district 
by manipulating {Normierung) the price, then local differences 
of profits will become regional factors of location for all stages 
of industrial production using coal. Thus, differences of profit 
may become locational factors. Nevertheless we can eliminate 
the varying rate of profit from consideration, for it is, like profit 
itself, not an element of the ''pure" economic order, but rather 
one of the capitalistic order. It does not concern us in pure the- 29 
ory. It is one of the alterations which the capitalistic order pro- 
duces in the pure order. 

The remaining elements of price (2-6) which are relevant 
for pure theory we may group more simply, i.e., more in accord- 
ance with the "natural" process of production. The second ele- 
ment, the interest rate on the capital employed, depends appar- 
ently upon two factors, the interest rate and the amount of 
capital. The amount of capital employed is apparently deter- 
mined by the prices of the various other elements of production 
(real estate, fixed capital (Stehende Sachkapitalien) , materials, 
wages, transportation rates). From this it follows that we may 
enumerate as (cost) elements of price the following as important 
for us : 

1. The cost of grounds. 

2. The cost of buildings, machines, and other fixed capital 
costs (Stehende Sachkapitalkosten) . 

clearly. It is necessary to keep this difference in mind for this discussion in which 
wages of management and payment of risk are part of the cost of production 
and not part of the profits. Weber is here, as throughout, concerned with the 
"pure" or "static" system of economics. Cf . above, p. lo. — Editor. 


3. The cost of securing materials, power and fuel. 

4. The cost of labor. 

5. The cost of transportation. 

6. The interest rates. 

7. The rate of depreciation of fixed capital.^ 
Which of these elements vary according to the location of 

the place of production and thus represent general regional fac- 
tors of location? Let us begin with the last one. 

1. The rate of depreciation (and therefore of amortization) 
of the fixed capital (7) is obviously on the whole independent of 
geographical situation. Only the climatic conditions may be of i 
importance, for example, by causing a greater amount of rusti 

30 upon the machines due to greater humidity of the air. But theses 
would be special, not general regional factors, and do not con- 
cern us here. 

2 . The interest rate (6) does not have locational significance« 
in connection with the process of production in the territory of an,; 
economically uniform state which we use as the theoretical basis- 
of our ''pure" theory. The interest rate varies, of course, accord- 
ing to the quality of the enterprise as well as the management;; 
thus the interest rate may certainly be higher as the consequence 
of a location which has been poorly chosen and yields a question- 
able return. But it does not vary according to regions within as 
given country as it doubtless does for different countries on ac- 
count of different security, different wealth, etc.^ It can never be 
the cause of regional choice of location in the pure economic sys- 
tem. In fact, it does not even show significant general differences 
between city and country, (i.e., between scattered and agglomer- 
ated industries) within such a political system as the German 

* It was only for the sake of thoroughness that we did not present this group- 
ing at the outset. 

® This aspect must be kept very clearly in mind in deaUng with locational 
problems in the United States. There is good ground for the assumption that 
these elements differ from state to state. — Editor. 


Commonwealth. It therefore does not even require consideration 
as an agglomerative factor which might operate within a given 
regional distribution of industry. 

3. The cost of land (i) varies in the case of industrial 
locations according to the amount of local agglomeration, but 
not regionally — at least not sufficiently to constitute a regional 
factor of location. In the case of land used for agriculture the 
price of land may exercise a regional influence. The prices of all 
other types of land have significance only in connection with ag- 
glomerations, for they represent nothing but results of agglomer- 
ation and deglomeration. The price of agricultural land may be 
in one part of the country about $50, in another, $150, in a third 
even $250 or $300 per acre, depending upon the density of pop- 
ulation. This will be a matter of great importance in determining 31 
the kind of agricultural production;" but for the choice of in- 
dustrial location it does not greatly matter, as it influences the 
price in much too small a degree. For example, if a modern spin- 
ning mill, which requires a great deal of space, needs 2 ^ acres 
for an annual production of 1,200 tons of yarn, it is almost neg- 
ligible whether $100^^ or $500 will have to be paid for this area. 

The additional $40 interest per annum cause an additional 
3.3 cents for each ton of yarn, the total value of which is from 
$240 to $800. This is such a small fraction that it is not im- 
portant as a locational factor. Even industries with a low-priced 
product and very large space requirements (such as iron works) 
are insensitive to these regional differences in the cost of land. 
Suppose, for example, a Thomas steel works which may be esti- 
mated to require 250 acres for an annual production of 300,000- 
I 400,000 tons^^ has to pay $250 instead of $50 per acre, and thus 

^° Cf. the classical treatment of Thünen, Der Isolierte Staat, Vol. I, which 
. deals with this problem. — Editor. 

I " Since this is an example only, dollars and cents and acres have been sub- 

stituted for Mark, Pfennig, and Aar on a rough average. — Editor. 

" Cf . Heymann, Die gemischten Werke im deutschen Grosseisengewerbe 
(München, 1904), p. 25. 


has on its books an item of $62,500 instead of $12,500 for 
land. The difference in interest on $1,250 per acre^^ causes a 
difference in cost of $0,005 per ton of product. Since this ton 
has a value of about $25, the difference amounts to two-hun- 
dredths of i per cent. This difference is much too small to exer- 
cise any influence upon the location. 

The situation becomes quite different if local agglomeration 
enters into the picture and suddenly creates those towering rises 
to $5,000, $10,000 and even $50,000 per acre.^* Such rises, of 
course, put the price of land among the relevant elements of cost 
of industrial production. For the Thomas steel works, for exam- 
ple, they would mean an increase in the cost of production on ac- 
count of rent (Preissteigerung durch Grundzins kost en) amount- 
ing respectively to $0.125, $0.25, and $1.00 per ton. These are 
amounts which certainly may be important, and on account of 
which the rent will codetermine the location for products of this 
32 kind. It is a locational factor within the agglomerative tend- 
encies. But it need not be considered for the regional factors. 

4. The cost of building, the cost of machines, and other 
equipment (2), and the cost of materials and power supplies 
(4), represent nothing but the results of the price-making of: 
(a) the production of raw materials and power supplies; (6) the 
previous and auxiliary stages of industrial production. 

Regarding b, they are for purposes of our reasoning funda- 
mentally the same thing as the particular stage of production 
which we have chosen for our abstract analysis. Their costs may 
be broken up into the same elements into which we have re- 
solved the costs of that stage. The previous stages contain no 

^•'Why Weber should use an interest rate of 2.5 per cent in this instance 
when he used 10 per cent in the previous one is not clear from the text. But the 
reasoning seems to hold good, even if the difference amounted to as much as 
0.08 per cent, as it would if an interest rate of 10 per cent were used. — Editor. 

" Cf ., for example, Andreas Voigt, Bodenbesitzverhaeltnisse, etc., in Berlin, 
regarding the rise in real estate values in Charlottenburg. 


new elements of cost, and thus no new and unknown locational 

Regarding a, there remain, then, as new elements of cost for 
our consideration the prices of raw materials and of power, and 
they in fact represent not only a new, but apparently a geograph- 
ically varying, element of cost, that is to say, a regional factor 
of location. The price at which the same material or power can 
be acquired may be and will be different at its various places of 
production, depending upon the nature of the deposit, the dif- 
ficulties of its mining, etc. Depending upon which particular 
"deposit," as we shall call it, one draws for his particular manu- 
facture, the costs of raw materials and power materials will 
vary. It will obviously depend upon the location of the plant 
whether it profits from the lower prices of a certain deposit of 
materials. Thus geographically determined differences of cost 
influence the location. These differences undoubtedly represent 
. the first general regional factor of location. 33 

I 5. The second regional factor of location are the regionally 
differing labor costs ( 5 ) . It goes without saying that their locally 
different level pulls production to and from certain regions. This 
is achieved by the costs of the manufacturing process (Stoffum- 
wandlung) within the stage of production here under considera- 
tion as well as indirectly by the prices of the auxiliary products 
which are partly determined by such labor costs. It should be 
, remarked, however, that we mean real labor costs. ^^ 
I 6. We come finally to the costs of transportation (6) which 
have to be met in order to assemble the materials and to ship the 
finished products. It is obvious that transportation costs will 
vary according to the location of the plant. They will vary ac- 
cording to the length and nature of the road which the materials 

^"The German text reads ". . . . dass natürlich nicht die absolute Höhe 
der Löhne dabei in Frage steht, sondern ihre Höhe bezogen auf irgend eine 
Einheit Produkt, das was man eben heute meint, wenn man präzis von "Arbeits- 
kosten" spricht. — Editor. 


have to travel from the place of production, and which the fin- 
ished products have to travel to their place of consumption. 
Sometimes the kind of transportation system will make a differ- 
ence. These costs, then, also are regional factors of location of a 
general kind. 


The relative price range of deposits of materials, the costs 
of labor and transportation, then, are the regional factors of lo- 
cation of every industry. Of these, we may for purposes of 
theoretical reasoning express one, the relative price range of 
deposits of materials, by another, by differences of costs of trans- 
portation. We shall thus simplify considerably the formulation 
of our theory, since we shall have to operate with only two re- 
gional factors. 

The different price levels of different deposits of the same 
material operate as if one had to oveicome different distances 
from these deposits to the place of manufacturing, or as if the 
''cheap" deposit were situated nearer the plant, and the "dear" 
deposit farther away. In order to see this clearly, one might 
imagine an average price as the normal price of each material at 
34 the deposit. The differences in the price at this or that deposit 
will mean the same thing, from the point of view of the indi- 
vidual plant, as if additional costs of transportation had to be 
paid. This means that the differences of the price of material 
deposits may be expressed abstractly as differences of cost of 
transportation. We need not treat them as a separate locational 
factor, but may introduce them later as a modification of the 
effect of the cost of transportation, a modification which, of 
course, will have to be elaborated considerably.^^ Consequently 
we may work with two general regional factors, the costs of 
transportation and of labor. 

This result is most important for us. Since we learned before 

" Cf. below, "approximations to reality," p. 74. 


that all general locational factors which are not of a regional 
kind (i.e., all the rest) can only be agglomerative or deglomera- 
tive factors, we may treat these latter factors as a uniform ag- 
glomerating force, that is, as a third uniform locational factor. 
We may thus at once construct our entire abstract system of 
general locational factors and the theory of its dynamics. 

Let us start by supposing that all the isolated processes of 
industrial production will ''naturally" at first be pulled to their 
most advantageous (optimal) points of transportation costs. Let 
us then regard this as the basic network of industrial orientation 
created by the first locational factor, transportation costs. Ap- 
parently, then, the differences of costs of labor (the second loca- 
tional factor) represent a force altering this basic network. The 
most advantageous places of labor costs create a first ''distor- 
tion" of the basic transportational (transportmässig) network of 
industrial location. We thus gain the conception of a fundamen- 
tal orientation of industry according to costs of transportation, 
and of an alteration of this fundamental orientation by "labor 
locations" (Arbeitsplätze). 35 

I Every agglomerating tendency — in other words, the entire 
'group of all other locational factors which we have not so far 
taken into account — is nothing but a second altering force, an- 
I other "deviating tendency" which tends to distort the transporta- 
tional network and shift it to certain other points, the "points 
of agglomeration." In its net effect this entire group is a "unit" 
also. And like the other "altering factor," the differences in 
labor costs, it is a uniform "locational factor." It is competing 
with that other factor. 

This completes the theory of general locational factors and 
the general survey of the dynamics within which they work, at 
least to the extent to which this theory and survey are necessary 
as a basis for the "pure" theory of location. There are no other 
general factors influencing the location of industry. The only 


question is to what extent and according to what laws these three 
factors control the various parts of the industrial system. To 
show this will be the task of the pure theory. By introducing the 
agglomerating factor into the explanation we seek to make an 
analysis of the general laws controlling the locational distribu- 
tion of industry, and not merely those connected with isolated 
36 processes of production. 




The theory to be given here is to explain reality. In the last 
chapter we have seen how complicated the reahty of industrial 
location is rendered by the interrelated working (Durcheinan- 
derwirken) of ''general" and ''special" locational forces. But 
this reality is further complicated by the fact that it results from 
the interaction {Hin- und Rückwirkung) of different economic 
spheres and of different parts of the same sphere. In our theory 
we shall ignore certain aspects of this situation. We shall assume 
that some of the facts which are in truth brought into existence 
by the processes which we analyze are independent of these 
processes. After having reached an understanding of the facts 
thus isolated, we shall introduce the full causal mechanism, i.e., 
we shall bring into proper perspective isolated data and shall 
analyze the change which is created thereby. 

On the basis of this method, industrial orientation will be 
further analyzed within the limits of the following suppositions : 

I. We shall assume the geographical basis of materials as 
something given. This assumption is in accordance with the 
facts when we are concerned with materials like stones, minerals, 
etc., which are simply dug out or mined — which, in other words, 
exist at different places by nature. The assumption is not quite 
so correct when the materials employed have to be produced, as 
is true of agricultural products. The agricultural basis of indus- 37 
trial materials is nothing "given." Agriculture receives its geo- 
graphical location by a peculiar process which itself depends 
upon the distribution of its products, that is to say, upon the 



orientation of industry. This has been elaborately shown by 

In placing industry for the time being theoretically into a 
given geographical ground plan of material deposits, we shall 
intentionally neglect the retroactive effect {Rückwirkung) which 
industry may exercise upon this ground plan. This assump- 
tion will have to be examined and brought into accord with 
reality later. 

2. The geographical nature of the sphere of consumption 
also will for the time being be treated as a given phenomenon. 
The situation and size of the places of consumption will be as- 
sumed in the pure theory as a given framework of orientation. 
We shall thus ignore the fact that each locational distribution 
of industry, merely by distributing the labor forces, distributes 
consumption of industrial products and of all other products. 
The geographical distribution of one sphere of consumption, 
which contains industry and its productive connections, is itself 
partly created and molded by this industry. 

3. Finally, we shall not introduce the mobility of the labor 
basis of industry. We shall operate with the schematic concept 
of an area covered by several fixed labor locations (Arbeits- 
plätze) instead of introducing the shifting distribution of hu- 
man labor characteristic of present-day reality.^ We shall fur- 
ther assume that the wages of each branch of industry are 
''fixed," while the amount of labor available at this price is un- 
limited.^ Here also we neglect in so doing a part of reality, for 
of course the locational tendencies of industry themselves create 
the standard of wages by codetermining the local demand for 

^Johann Heinrich von Thünen. Der isolierte Staat in Beziehung auf Land- 
wirtschaft und Nationalökonomie (Rostock, 1842). Cf. p. xix. — Editor. 

^ This is the point of attack of Sombart. Cf. Der Moderne Kapitalismus, 
Vol. II, 2 and above, p. xxv. 

^The details regarding these suppositions and the reasons for them, may 
be found in chap, iii, sec. I, toward the end. 


labor. Moreover, we disregard for the time being to what extent 38 
the local distribution of labor, i.e., the situation and size of labor 
locations, is generally influenced by the other locational tenden- 
cies of industry. We evade all these problems for the moment by 
assuming a given basic distribution of labor. It should be said at 
once that it will become apparent that this third assumption can- 
not be eliminated within the scope of the ''pure" theory; the dy- 
namic relationship between the local distribution of labor and the 
locational tendencies of industries can be explained only by the 
realistic theory. 

Other assumptions and simplifications will appear necessary 
from time to time, but all of them will accompany us for but 
short distances. Only the three simplifying assumptions just 
mentioned are permanent and constitute the matrix within which 
the pure theory will be found. 


As the foregoing analytic examination of the locational fac- 
tors shows, we assume in our theory that all industrial produc- 
tion is dependent upon the use of ''materials," which are either 
raw materials, half-finished products, or power supplies (wood, 
coal). We speak exclusively of the use of "transportable" ma- 
terials. In fact, however, not only materials enter into produc- 
tion, but "forces of nature" as well. They are used as live energy: 
either given by nature, like water power, or transformed, like 
electricity. The question is whether a theory which employs the 
concept of transportable materials only can include the loca- 
tional effect of those other forces as well. The answer is that 
apparently it is possible to treat these forces of nature with re- 
gard to their locational influence, as if they were especially cheap 
coal deposits. If that is done — how it has to be done is shown in 
the last sections of the chapter on transport orientation — we 39 
shall get rules determining the locational importance of these 


forces. These rules modify only slightly the general rules which 
apply when transportable materials are employed. 

Thus no specific effect which could not be fitted into the the- 
ory remains. This theory, then, embraces in its simple mold in- 
dustry in its entirety, with all the materials and forces which it 
40 absorbs into itself. 






The problem to be solved is how transportation costs in- 
fluence the distribution of industries, assuming that no other 
factors influencing the location of industry exist. To what places 
will industry be attracted? It is clear that it will be drawn to 
those locations which have the lowest costs of transportation, 
having regard both for the place of consumption and the place of 
the deposits of materials. Where are these places? At first we 
shall locate them in very general terms, and to that end we in- 
quire: On what basic elements do transportation costs depend? 

The fundamental factors which determine transportation 
costs are the weight to be transported and the distance to be 
covered. Since these two factors may readily be defined in math- 
ematically exact terms, they provide a definite basis for an ab- 
stract theory, leading possibly to mathematical formulas. We 
shall, at the outset, treat these two factors as the only determin- 
ing factors. This procedure is justified because we are thinking 
of costs in an economic sense. There are, of course, two kinds of 41 
"transportation costs:" transportation costs in the sense of pohti- 
cal economy, and transportation costs as understood by the busi- 
ness man paying for the shipment of goods. The former costs 
are the total amount of goods and labor that are absorbed in 
effecting such a shipment. The latter costs are the monetary pay- 
ment made to those furnishing the transportation.^ If we speak 

^ This, in English terminology, would commonly be termed the rate or the 
price of transportation. Cf . also Emil Sax, Die Verkehrsmittel, 2d ed, I, 76 ff. The 



of weight and distance as the fundamental factors determining 
transportation costs we obviously have in mind the costs of 
''pure" political economy. 

Our further discussion is based upon the possibility of ex- 
pressing in terms of weight and distance all other factors which 
contribute to the cost of transportation, limiting our considera- 
tion to an area with a uniform system of transportation. Because 
of this possibility we are able to reduce the other factors theoret- 
ically to these two. 

What this means and why it is the case requires a brief ex- 
planation. In this connection it should be noted that the trans- 
portation system analyzed here is the railway system prevailing 
today and the particular rate structure existing in Germany. The 
railroad system has been chosen for our analysis of the causal 
relationship between the cost of transportation and the distribu- 
tion of industries over a territory because the railroad is today 
the chief means of transportation by land. As a device for simpli- 
fying our problem, we shall proceed as if it were the only system 
42 existing.^ The significance of the relationship between carriers 
subject to different principles of cost determination will be ex- 
amined later when our abstractions are brought into accord with 

It is clear that the cost of transportation depends upon the 
following factors, besides weight and distance: ( i ) The type of 
the transportation system and the extent of its use; (2) the na- 
ture of the region and its kind of roads; (3) the nature of the 
goods themselves, i.e., the qualities which, besides weight, deter- 
mine the facility of transportation. 

problem of joint cost is discussed by F. W. Taussig, "A Contribution to the 
Theory of Railway Rates," Quarterly Journal of Economics, V, 438, and A. C. 
Pigou, The Economics of Welfare, p. 266-68. — Editor. 

^The same analysis could be undertaken for any other rate structure and 
any other system of transportation, but it is not necessary, because the prin- 
ciple is the same everywhere. 


Taking up the first point, it hardly needs to be explained that 
the type of the transportation system and the extent of its use 
produce great differences in cost as among the different systems. 
A given weight is carried a given distance today on railroads for 
one-quarter to one-tenth of the rate prevailing when carriages 
had to be used. The costs must have dropped correspondingly. 
However, different systems of transportation do not concern us 
for the present, since we are assuming a uniform system. 

But even in a uniform system the different parts of the sys- 
tem are used with varying intensity, and this varying intensity 
causes differences in the cost of transporting a given weight a 
given distance. The shipping of one hundred tons of coal costs 
more on a road when a special freight train must be made up for 
the purpose than when an existing train can carry an additional 
hundred tons. Similarly the costs will be higher when there is 
no return freight than when return freight is always available. 
So also the costs per ton-mile vary, even on the same road, ac- 
cording to the volume of traffic. These are well-known facts. It 
is also known, however, that it is so difficult^ to calculate individ- 
ually the resulting differences in the cost of shipping individual 
articles, that these differences are disregarded in the rate-making 
of our present uniform railroad system, and the rates are fixed 43 
uniformly per ton-mile for all Hues. Since, in making its rates, 
our system of transportation disregards these variations from 
a cost caluculated according to weight and distance, they may be 
disregarded in our theory. But if in fact such variations of rates 
should exist, the problem arising should be solved by assuming 
that lines with higher rates are prolonged in proportion to the 
higher rate; and similarly, lines with lower rates should be as- 
sumed to be shortened. If, for example, on certain lines a one- 
and-a-half rate per ton-mile is collected instead of the normal 
rate of one, such lines should be regarded as one-and-a-half times 
as long as they really are in applying to them a theory of location 

^ For this point, cf . Taussig. — Editor. 


which assumes uniform rates. In Germany conditions do not, 
on the whole, call for this method of treatment. 

There is, however, another aspect to this matter, an aspect 
in which the interest of the carriers in the greatest possible utili- 
zation of their facilities is reflected in the rates. Higher rates per 
mile prevail generally for small shipments and for shipments 
over short distances. This is not the place to show how and when 
these adjustments result from the necessity of increasing the 
density of traffic, nor to show how they relate to the lowering of 
general operating expenses per unit carried. Since such adjust- 
ments do exist, the problem they place before us is this: How 
may they be disposed of in treating cost of transportation merely 
as a function of weight and distance? 

No serious problem is raised by rates which decrease as the 
distance increases. The same theoretical principle as before can 
be used here; the distance can be thought of as varying accord- 
44 ing to the percentage of the decrease whenever such scales apply. 
Geographical distances should not be measured by their geo- 
graphical length, but in proportion to the decreasing rate scale.* 

The problem raised by the difference in rates between par- 
cels, half-carloads, and full carloads, is best solved by regarding 
those charges which are made on full carloads as the normal ton- 
mile rates. Then those goods which are charged higher rates 
because they are shipped in small quantities can be regarded as 
possessing an ideal weight in addition to the real weight. For in- 
stance, if the normal rate for full carloads is 6 cents, the rate for 
half-carloads 6.7 cents, and the rate for parcels, 11 cents, goods 
not shipped in full carloads may be regarded as having an addi- 

* If, as in the case of parcel rates in the general class in Germany, a rate of 
II pfennig is charged per unit of weight for 50 kilometers, 10 for the next 150, 
and 9 for the next 100, and so on, a stretch of 100 is counted as=5o4- (So- 
50/11) = 95.4 km. We may say, then, that the geographical distance is corrected 
in proportion to the rates; an operation which, by the way, the present German 
rate structure fortunately spares us to a large degree. It provides a graded scale 
of rates only for some of the parcels and for a few bulk goods. 


tional "ideal" weight amounting to i.i per cent and 83.3 per cent 
respectively of their real weight. Similarly, the weight of goods 
shipped on special reduced rates may be thought of as being re- 
duced in proportion to the reduction in rates. 

In this way it seems possible for theoretical purposes to ex- 
press in terms of weight and distance all variations in rates, and 45 
thus to fit them without difficulty into a theory based on weight 
and distance alone. The general principle of this approach to the 
matter is clearly based on the fact that the effect of all elements 
of cost will appear as increase or reduction of the rate per ton- 
mile. This justifies operating theoretically with weight and dis- 
tance, the two basic elements of the cost of transportation. 

In passing we may apply this method to the other two most 
important instances of variations of cost as mentioned before. 

The second factor upon which cost of transportation de- 
pends, aside from weight and distance, is the nature of the local- 
ity, influencing the road bed (see p. 42). On the one hand the 
nature of the locality determines the cost of road construction, 
and on the other hand it affects the cost of operation. Obviously, 
these local increases or decreases of cost, reflected in ton-mile 
rates, may be expressed by prolonging or shortening the sections 
in question proportionally. They therefore offer no particular 
difficulty for our theory. Moreover, the management of modern 
railway systems operated under consolidated control usually 
ignores these differences in cost. For instance, rates in Germany 
are uniform, regardless of the special cost both of construction 
and of operation of different sections of the system. In our later 46 
inductive examination of location we are not dealing with moun- 
tains and valleys, but with a mathematically flat plain where the 
mountains are razed, the valleys filled, and the swamps covered. 
The rate structure of the German railroads realizes the "ideal"; 
we shall utilize it in our work and thus simplify our deductions. 

The third factor affecting cost of transportation, aside from 
weight and distance, is that of special qualities of the goods trans- 


ported. Bulky goods require more space, and thus increase the 
cost by requiring more rolling stock. Perishable and explosive 
goods necessitate great care, not only in loading, but also in car- 
rying them. All such qualities result in higher rates per ton. 
Moreover, certain kinds of goods are given higher rates, which, 
because of the high value of the goods, do not increase costs par- 
ticularly. Indeed, there exist systems of rate-making which, 
disregarding weight, take for their basis value and distance. In 
fact, however, all so-called value rate-schedules {Werttarife) are 
really based on weight, even though disguised by scales of value. 
But it does not concern us here whether scales based on value are 
justified, since the transportation of an object requires the same 
cost whatever the value.^ Suffice it for us to know that such 
scales exist. They do not cause us any difficulty. An increase in 
47 the rate per ton-mile, no matter for what reason, means added 
''ideal" weight, a decrease means subtracted "ideal" weight; that 
is all.^ 

All the foregoing is perfectly simple. We have not only dem- 
onstrated clearly the principle in accordance with which the im- 
portant factors determining cost may be expressed in the two 
basic factors of weight and distance, but also the practical exe- 
cution of this principle for all cases important in the making of 
railway rates today. The only question that might be raised is 

^ Cf. for this discussion, Sax, Verkehrsmittel, p. 76 ff. and 100 ff., and par- 
ticularly F. W. Taussig, op. cit.; also J. W. Clark, The Economics of Overhead 
Costs. — Editor. 

* The German railway freight tariff assigns to "bulky goods" one and one- 
half times their actual weight, and we may consider them as having this weight. 
In the German system, value is taken into consideration when certain commodi- 
ties of low value are shipped at lower rates than is usual. Thus certain parcels 
of low value are shipped at 8 pfennig instead of 11, and carloads of certain goods 
of small value at 4.5, 3.5, and 2.6 instead of 6 pfennig. Here again, subtractions 
in weight may be made in our calculations corresponding to these reductions ; for 
instance, coal, which is shipped at 2.6 pfennig instead of 6 pfennig may be rated 
as if it had lost 56 per cent of its real weight when we come to applying our 
theoretical findings to German reality. 


whether the deviations from the uniform rate based on weight 
and distance and the adjustments resulting therefrom are not so 
large (particularly in other transportation systems) that it is 
impractical to express theoretically all transportation costs in 
weight and distance. In answer to this we may say two things : 

First, weight and distance are not only the basis of railroad 
rates but are the predominant factors in the cost of transporta- 
tion, and hence of rate-making in any system, since they largely 
determine how much labor is necessary. This labor, regardless of 
its nature, is the essential factor of cost, and consequently of rate- 
making. An abstraction based on it is accordingly in no real 48 
danger of giving a distorted picture of reality through being dis- 
torted by the influence of other factors. 

Second, the rate structure as it exists in Germany today ap- 
proximates closely the abstraction just made. The German rail- 
roads use the ton-mile rate as the general basis, calculating rates 
according to weight and distance. The whole country, as has 
been said before, is regarded as a mathematically flat surface. 
They employ merely "ideal" weight additions (Gewichtszu- 
schläge) for half -carloads and parcels, as well as for bulky and 
explosive goods; and on the other hand they employ ''weight re- 
ductions" (Gewichtsabzüge) for the large and important classes 
3f goods of low value. They employ special rates modifying the 
jniform ton-mile rates only for certain sections, and, as men- 
ioned before, a restricted use is made of decreasing scales with 
ncreasing distance for parcels and a few bulky goods of low 

Reality, then, will not be too greatly distorted by our ab- 
straction. It seems quite admissible to work with weight and dis- 
ance in theory as well as in practice; in short, to work with the 
on-mile rate as the basic scale of transportation costs, at least 
n a territory with one uniform system of transportation. The 
ustification in both theory and practice for this simplifying as- 
umption of the existence of a uniform system of transportation 


may be taken for granted for the time being, for we shall show 
later on that the more complicated situation of several co-operat- 
ing transportation systems can also be explained in accordance 
with the theory here developed. 



If weight and distance are the only two determining factors, 
evidently transportation costs will draw industrial production to 
those places where the fewest ton-miles originate during the en- 
tire process of production and distribution; for with production 
at these places the costs of transportation will be lowest. 

But how will the places of minimum ton-miles actually dis- 
tribute the production? That is the real question to be answered. 

In order to answer it, the simplifying assumptions of the 
whole theory set forth in the last part of the preceding chapter 
must be kept in mind. We are to regard as given the location and 
the size of the places of consumption of each kind of produc- 
tion; and we are to regard as given the location of the available 
material deposits. Furthermore, for the time being (up to chap, 
vi) we proceed upon the assumption that each product will be 
produced in one stage of production, the raw material being 
turned into the finished product at some single place of produc- 


Let us then imagine ourselves stationed at some one of these 
given places of a given amount of consumption. Clearly, viewed 
from this place, there must be for every kind of product con- 
sumed at this place certain deposits of materials (raw materials., 
power materials) the use of which will result in the lowest trans- j 

50 portation costs. 

By no means will these deposits necessarily be those locatec 
nearest to the place of consumption. It is possible that in the 


case of certain materials a position near deposits of other ma- 
terials is more important (bearing in mind the cost of transpor- 
tation resulting from the whole process) than a position near the 
place of consumption. In such a case that position will be chosen 
which is optimal. In any event, viewed from each place of con- 
sumption, there doubtless exists for each kind of product a most 
advantageous location of each material that is utilized in making 
the product. Obviously, the deposits thus most advantageously 
located will be employed for such production as is necessary to 
fulfil the demand at the particular place of consumption. The 


Fig. 2 Fig. 3 

location of the place of production must be determined somehow 
in some relationship to the place of consumption and to these 
most advantageously located material deposits. Thus ''locational 
figures" are created, one for each place of consumption of each 
product. This locational figure is formed (as indicated above) 
by the place of consumption and the most advantageous mate- 
rial deposits. Each product will somehow select its place of pro- 
duction (location) in terms of this figure. 

Let us suppose, for example, that we are dealing with a prod- 
uct composed of two materials which are to be found in scattered 
deposits. In such a case the "locational figures" would be repre- 
sented by triangles. One comer of each triangle would be the 
Dlace of consumption, and the other two corners would be the 
two most advantageous places of material deposits, as shown in 
figures i, 2, and 3. 

Assuming that nothing but the cost of transportation influ- 
ences the selection of the location, it is evident that these loca- 


tional figures must give the only possible mathematical basis of 
orientation. This presupposes, however, that location could be 
divided, as a matter of analysis, into just as many parts as the 
locational figures contain. We can presuppose this because we 
are disregarding for the present all agglomerating and deglomer- 
51 ating factors. 

These 'Vocational figures" therefore represent the first and 
most important basis for formulating {vorstellen) the theory. 
We shall apply these figures to the most complicated sets of facts 
because through their use the outstanding elements of the struc- 
ture of orientation are laid bare. 

How is production oriented in terms of these locational fig- 
ures? A general observation must be made before proceeding to 
answer this question. The main features of the orientation of 
production must be the same in all individual locational figures, 
no matter what the industry may be. For in all of these figures 
the main features of the orientation of production depend upon, 
and are determined by, the nature of the transportation needed 
for the particular industry. It follows that in order to find the 
principles according to which one may locate the theoretical 
point where transportation costs are lowest, it is sufiicient in a 
theoretical analysis to deal with a single locational figure. 

Then, too, before we can go on we must introduce some new 
terms. They refer to the nature of the materials employed by 
industry: (a) the nature of their deposits, and {b) the nature 
of their transformation into products. It will become apparent 
that the ''transportational nature" of various industries depends 
entirely upon these facts. 

As regards the nature of the material deposits, some ma- 
terials employed in industry appear everywhere; they are, for 
practical purposes, put at our disposal by nature without regard 
to location. When the whole earth is considered this actually 
holds true only in the case of air; but when more limited regions 
are considered, it holds true for many other things. Brick-clay. 


wood, grain, etc., are materials available practically everywhere . 
in certain regions. Such materials will be called ''ubiquities"; in 

I the former case ''general," in the latter, "regional." Naturally 
they will be available or producible in each place only in limited 
quantities ; nevertheless it is possible that the local demand does 
not exceed the limits of their supply, and in that case they are 
practically "absolute ubiquities." If the demand does exceed 
this limit, they are "relative ubiquities" for the place, the region, 
etc. Thus, water is a practically unlimited, and therefore an 52 
"absolute" ubiquity in many German regions; hkewise brick- 
clay for certain large regions. Grains, on the other hand, are 
naturally only "relative ubiquities" for all territories which im- 
port grains. "Ubiquity" naturally does not mean that a commod- 
ity is present or producible at every mathematical point of the 
country or region. It means that the commodity is so extensively 
available within the region that, wherever a place of consump- 
tion is located, there are either deposits of the commodity or op- 

iportunities for producing it in the vicinity. "Ubiquity" is there- 
fore not a mathematical, but a practical and approximate, term 
(praktischer ''Näherungsbegriff'') J 

Other materials are not obtainable in the vicinity of a place 
of consumption (irrespective of where it may lie within the coun- 
try or the region which is made the object of locational analysis) , 
but only in geographically well-defined localities. Or, if they are 
technically obtainable, they are in fact mined or are produced by 
agriculture only in well-defined locaHties because of economic 

: reasons. We find that minerals and coal, as well as most of the 
.substances which are used for chemical and china manufacture, 

1 jbelong in the former category of technically locahzed materials, 
while wood and wool belong in the category of the economically 
ocaHzed materials. 

It is obvious that it is not predetermined for all time whether 

'Regarding O. Englander's critical discussion of this concept cf. above, p. 
Kiv, n. 31. 


an industrial material is "localized" or "ubiquitous"; this must 
be determined within each area, country, or region, for the period 
which is made the object of locational analysis. Let us take for 
example the southeast of the United States. For that region 
(perhaps! ) cotton is ubiquitous from a practical standpoint; but 
evidently it is not ubiquitous for the world at large. For Ger- 
many cotton represents the reverse of a ubiquity; it is a material 
which must be brought in from very distant places outside. It is 
evident also that all relatively ubiquitous materials belong in the 
sphere of localized materials if at a given place the demand for 
them or for any of their parts exceeds the amount obtainable at 
53 that place. Barley is a case in point in so far as the demand for 
it in breweries exceeds the production within the "vicinity" of 
the brewery. 

As regards the nature of the transformation of materials into 
products, a material enters into a product either with or without 
residues. These residues may be used for another product, but 
they are refuse from the point of view of the first product. In 
order to have a term for this distinction we may speak of "pure 
material" and "gross material." Any ubiquitous material can 
naturally be either pure or gross. But since this distinction has 
no significance for location in the case of the ubiquities, the 
terms "pure material" and "gross material" will, for the sake of 
brevity, be used only for "localized" materials. 

Another distinction may be made regarding transformation 
of material into a product, as follows: "pure material" imparts 
its total weight to the product; "gross material," only a part of 
it. Consequently we may consider fuels (such as wood, coal, 
etc.) when used for production as the extreme case of gross ma- 
terials, for not a single bit of their weight enters into the product. 
They create important chemical and mechanical changes, but 
their use adds no weight to the product; their entire weight, from 
the point of view of the location, remains behind — "outside." It 
is desirable for our purposes that such materials be classified 


under the general heading of "weight-losing" materials, together 
with the other gross materials which technically play a funda- 
mentally different role in production. There are therefore two 
kinds of gross materials: the fuel which leaves its total weight as 
a residue outside of the product, and the gross materials which 
leave only a part of their weight. It is apparent that it is very 
important for our theory to have covered these two distinct kinds 
of materials with one term, for the simple reason that we are 
dealing at present with the effects of weight only. 54 

The materials used by industry are, for the purposes of the 
following analysis, either "ubiquities" or "localized materials"; 
and these latter either "pure materials" or "weight-losing ma- 


We have said that production will be oriented, under the in- 
fluence of costs of transportation, in terms of the "locational 
figures" which we have discussed. In view of our explanation of 
I these figures, this statement means that production must find the 
points of minimum ton-miles. These points will be the trans- 
portational locations. 

How are they to be found? The fact from which we start is 
that such a location, wherever it may lie, always shows the fol- 
lowing transportational relations: the entire weight of the ma- 
terials which are used in the production must be moved to this 
location from the material deposits; and the weight of the prod- 
uct must be moved away from this location to the place of con- 
sumption. This means that this location is connected with the 
"corners" of the locational figures by lines along which move the 
weights which appertain to these corners (the weights of the 
material and the product respectively). Along the lines — let us 
icall them "components" — of the material deposits run the re- 
spective material weights, and along the component of the place 


of consumption runs the weight of the product. Let us imagine 
a process of production which uses two locahzed materials, three- 
fourths of a ton of the one and one-half ton of the other being 
necessary in order to produce one ton of the product. The loca- 
tional figure shows the weights three-fourths and one-half mov- 
ing along the components of the two materials; while the com- 
ponent of consumption carries the weight one. (See Fig. 4, p. 


These weights represent the force with which the comers of 
the locational figures draw the location toward themselves, it 
being assumed that only weight and distance determine transpor- 
ts tation. For any movement of the location along a component 
toward a corner saves just as much as the movement amounts to 
in ton-miles. And if orientation takes place solely in accordance 
with ton-miles, the importance of every corner will be propor- 
tional to the ton-miles which can be saved by approaching it, i.e., 
the distance between the location and a given corner will be de- 
termined by the weight which attracts along its locational com- 
ponent. It follows as a general principle that the location will be 
near the individual corners or jar from them according to the 
relative weight of their locational components. 

The mathematician (cf. Mathematical Appendix I, §2) tells 
us that the precise location within the figures can be determined 
mechanically by means of a frame (Varignon's frame; cf. picture 
in Appendix p. 229). The corners of this frame are to be set up 
at the corners of the locational figure. Over these corners run 
threads on rollers, the threads being loaded with weights propor- 
tional to the weights of the components. In the inner part of the 
figure these threads are connected at some point. Wherever this 
connecting point (which must be prevented from being drawn 
beyond one of the corners) comes to rest, there is the location. 
This location point may be in one of the corners, if one of the 
weights is of the necessary size, or if a peculiar geographical con- 
dition prevails ; otherwise, it will be found somewhere within the 




On the basis of the same general concept (Allgemeinvor- 
stellung) in accordance with which the location is mechanically 
determined, '^weight figures" can be mathematically deduced for 
any kind of production. While the locational figures will always 
be individual or specific for a particular plant, these weight fig- 
ures are general, applying to all plants of the same kind of pro- 
duction. Such weight figures are formed by line segments whose 

Fig. 5 

Fig. 6 

length is proportional to the size of the weights which attract 
along the components of the locational figure of a particular 
productive enterprise. If the locational figure is a triangle, and 56 
if, as in the previous example the component weights are i=ai, 

J4=a2, y2=(i3, then we can construct a weight figure which 
looks like Figure 5. 

The following propositions regarding the position of the lo- 
cation can be deduced mathematically : 

I I . If it is impossible to form a figure out of the linear seg- 
ments corresponding in length to the component weights, i.e., if 
one segment is as long or longer than all the rest together, the 
location always lies in the corner of this component. This becomes 


evident by merely observing the mechanics of the "weights"; 
for if the one pulling weight is as great or greater than all the rest 
put together, it cannot be moved by them from its corner. 

2. If, however, a weight figure can be constructed, i.e., if no 
one weight is as great or greater than all the rest together, the 
locational figure becomes important. If the locational figure 
is as simple as a triangle, we can discover the location by a 
simple construction (cf. for the mathematical analysis Appen- 

57 dixl,§4). 

The general meaning of this construction is that two "cor- 
ners of the locational figure" can always be seen from the loca- 
tion at an angle, the size of which depends upon the relative size 
of the component weights of these corners (in comparison with 
the component weight of the other corners). If the relative size 
is large, the angle will be large; and therefore the location lies 
upon a lower arc connecting the two corners, thus being neces- 
sarily close to the corners. And vice versa, if the relative com- 
ponent weight of the corners is small, the angle will be small 
also ; and the location lies upon a higher arc connecting the two 
corners. The location will thus probably lie jar from both cor- 
ners, and certainly far from the weaker of the two. This de- 
scribes in exact terms how the relative size of the weights affect 
the location with respect to the position of corners. 

There is one more remark to be made. The third corner may 
lie within the determining arc which contains the other two, so 
that the determining arcs intersect each other, not within, but 
outside of, the locational figure (see Figs. 7 and 8). That occurs 
either when the component weights of two corners in comparison 
with the third are small, and the determining arc therefore ex- 
tends very high over them (Fig. 7), or when the third corner 
lies near the connecting line of the other two comers (Fig. 8). 
In these cases the location does not move beyond this inclosed 
comer, but lies at this corner as in the first case when the weight 

58 of this comer entirely preponderates (see Appendix I, §7). 


Three cases may be distinguished if the locational figure is 
a triangle : 

In the first case, the weight appHcable to one comer is equal 
to or larger than the sum of the other two weights ; then the loca- 
tion always lies at this corner. 

In the second case, the weight applicable to the one corner 
is not equal to or larger than the sum of the other weights, but 
it preponderates considerably. If this corner does not lie too far 
away, it is likewise the location.^ 

In the third case, the point where the "determining arcs" 
intersect is the location. It lies near any two corners, or far from 

Fig. 7 Fig. 8 

them, according to the size of their weights, compared with the 
weight of the third corner. 

3. For all locational figures other than triangles, we do not 
have any such simple method of determining the location (see 
Appendix I, §12). The mechanics of the described frame of 
Varignon offer the easiest way for determining it. We can, how- 
ever, imagine that the location is pulled toward any two corners 
of a given locational figure according to the relative size of their 
component weights, and we can thus apply the general idea 
gained from the triangle to these more complicated figures; al- 
though the pulling forces cannot be so easily expressed mathe- 
matically as in the case of the triangle. Although high or low 
arcs no longer afford a mathematical expression of the location 

* Under this case comes also the instance of a close geographical proximity 
of the third corner, but this instance will be disregarded for the present. 


being pulled to any two corners, nevertheless the foregoing fur- 
nishes a basis for a general picture of where the location lies in 
these complicated figures. 


What follows from these simple mathematical conclusions 
as regards reality? Do they cover reality completely? 

For all cases in which localized materials are employed, the 
foregoing obviously furnishes a sufficient explanation as to where 
the location will lie. Whether a complicated locational figure 
results from the employment of numerous materials, or whether 
a simple triangle results from the use of only two materials, or 
whether finally the employment of a single material causes this 
locational figure to shrink to a ^'line" which connects the one 
material deposit with the place of consumption, the mechanics 
59 will always remain the same. The material deposits will pull 
with the weight of the material, the place of consumption with 
the weight of the product, and the location will be determined 
in the manner which has been discussed. The determining me- 
chanics are simplified, however, when tlie "figure" shrinks into 
a Hne — the only two existing components (that of the one ma- 
terial deposit and that of the place of consumption) coinciding 
and thus connecting the two places. Along this straight hne the 
weight of the material will pull in the one direction, the weight 
of the product in the other; and the preponderance in weight of 
the one over the other will determine where the location lies upon 
the line. This means that the location will be at the "deposit" in 
case the material has the larger weight, and at the place of con- 
sumption in case the product has the larger weight. In case the 
weights are equal, the location will be anywhere on the line. 

When localized materials are employed, what will be the re- 
sult if ubiquities like water are used in addition? This question 
arises if any increase in weight of the product over and above the 
used weights of localized material results from the use of ubiq- 
uities, as was assumed previously. The ubiquities have no defi- 


nite deposits which could influence the locational figure; they are, 
according to their very definition, present everywhere. Their 
effect seems at first thought to be altogether beyond analysis by 
locational figures; however, that is not the case. Since they are 
available wherever production may take place, they will in fact 
be obtained wherever the location is, which means that they will 
exert an influence upon the locational figure, not as a material, 
but only in their manufactured form within the product. They 
become significant for locational purposes only because they in- 
crease the weight of the product. In other words, they affect the 
locational figure simply by strengthening the component of the 
place of consumption (which goes from the location to the place 
of consumption), because they add to this component their 
weight — a weight which had not previously appeared. 60 

When we reflect upon this we see that the theory fully covers 
reality ; it covers the case of both locaHzed materials and ubiq- 
uities. Evidently it should be possible to develop out of this 
theory all variations of reality. 


So far as transportation is concerned, we might look upon 
the process of determining location as a struggle between the 
different corners, i.e., between the corner of consumption and the 
comers of the materials. What determines the outcom.e of this 
struggle? Perhaps, one might think, the extent to which material 
is used in the manufacture of a product, and therefore the num- 
ber of tons of material which are required for one ton of product. 
Or, what would be the same, the extent of the losses of material, 
productive processes with many tons of material per ton of 
product being oriented near the material, and other types of 
productive processes being oriented near the place of consump- 
tion. Judging from our previous conclusions, that is incorrect. 
The same quantity of coal or other weight-losing factors may be 


employed per ton of product in two cases and yet the two loca- 
tions may lie at entirely different points in the locational figure; 
indeed, in one case at the place of consumption, in another case 
at the deposit or near the deposits. It depends upon how strong, 
relatively, the component of the place of consumption is — pos- 
sibly as strenghtened by ubiquities. 

The determining factor is not the proportion of the weight 
of used material to the weight of the product, but the proportion 
of the weight of used localized material to the weight of the prod; 
uct, all ubiquities being of importance only as they increase this 
weight of the product. This proportion of weight of localized 
material to weight of product we shall term "material index" of 
production. Consequently a productive process which, for ex- 
ample, uses one ton of localized material plus half a ton of ubiq- 
uities for one ton of the product has a "material index" of one; 
so also has one which uses a whole ton of ubiquities in addition 
6 1 to one ton of localized material (for example, a ton of earth in 
addition to one ton of coal); and so also, of course, has one 
which uses simply one ton of pure material. Abstractly speaking, 
they are all oriented alike. 

If we thus call the proportion of the weight of localized ma- 
terial to the weight of the product the "material index" of an 
industry, one may say further: the total weight per unit of prod- 
uct to be considered for the movement within the locational 
figure in any kind of productive process apparently depends 
simply upon this material index of the industry. For this ma- 
terial index indicates how many weight units of localized ma- 
terial have to be moved in the locational figure in addition to the 
weight of the product. The material index measures the total 
weight to be moved. This total weight to be moved in a loca- 
tional figure per unit of product we shall from now on call the 
"locational weight" of the respective industry. It is evident that 
this locational weight has the minimum value i when the ma- 
terial index (M.I.) has the value o (which it would have when 


ubiquities only had been used), and rises parallel to the material 
index: M.I. = y2, L.W. = iVi, etc. 

We now can state the following conclusions regarding the 
struggle with respect to location between the place of consump- 
tion and the material deposits. 

First, generally speaking, industries having a high locational 
weight are attracted toward material; those having low loca- 
tional weight are attracted toward consumption; for the former 
have a high, the latter a low, material index. In view of our 
mathematical conclusions, then, all industries whose material 
index is not greater than one and whose locational weight there- 
fore is not greater than two lie at the place of consumption. 

Second, with respect to the composition of the material index 
we can deduce the following: Pure materials can never bind pro- 
duction to their deposits. For since they enter without loss of 62 
weight into the product, the sum of the component weights of 
their deposits is always at most equal to the weight of the prod- 
uct, and therefore the material index which they create never is 
more than one. We shall see the details below. Weight-losing 
materials, on the other hand, may pull production to their de- 
posits. For this to happen, however, it is necessary that the 
material index which they codetermine be greater than one, and 
that their portion of the material index be equal to that of the 
remainder plus the weight of the product. Stated more simply, 
their weight must be equal to or greater than the weight of the 
product plus the weight of the rest of the localized materials. 


Let us now analyze the various possible cases of reality, and 
let us attempt to exhaust all possible combinations. The follow- 
ing possible combinations of materials in the various industries 
are to be considered: (i) use of ubiquities only, (2) use of lo- 
calized pure materials alone or with ubiquities, (3) use of weight- 
losing materials alone or with other materials. 


1. Ubiquities only. — {a) One ubiquity: In this case pro- 
duction will always choose its location at the place of consump- 
tion. Our theory shows that the locational figure shrinks into 
one ^'point," the place of consumption at which production must 
occur. It is obvious from the facts; for if production occurs at 
the place of consumption, there is nothing at all to be trans- 
ported, while any other location would necessitate transportation 
after the production, {b) Several ubiquities: There appears to 
be no reason why the location should be chosen elsewhere than 
in the case of only one ubiquity; the location will lie at the place 
of consumption. 

2. Localized pure materials either alone or with ubiquities. 
63 — a) If one pure material is used alone, the locational figure 

shrinks to a ''line"; as mentioned before, the line from the de- 
posit of the material to the place of consumption. Along it pull 
the weight of the material and the weight of the product in oppo- 
site directions. In this case the material index is equal to one, , 
since the material enters in its entirety and no further material is 
added and the two weights are equal. The same weight is to be 
transported whether production is carried on at the place of con- 
sumption, at the material deposit, or somewhere in between. 
The location is mobile; it may lie at any point along this "line" 
or at one of its two termini, the place of consumption, or the 
material deposit. 

b) If ubiquities are added the location is affected. The ma- 
terial index is less than one; the component of the material de- 
posit is smaller (just by the ubiquities) than that of the place oi 
consumption; and the location is therefore situated at the latter, 

c) In the case of several pure materials alone, the material 
index is again equal to i. According to our theory, therefore, 
the location should be at the place of consumption; for the ma- 
terial index does not pull the weight of the product along one 
line, but along as many different lines as there are materials. Nc 
single one of these components is equal to the component of the 


place of consumption; the latter is as large as all of them to- 
gether. It therefore keeps the place of production at the place 
of consumption. This may also be established by another Hne of 
reasoning. The weights of all materials, whether in the form of 
materials or in the form of product, have to be moved from their 
deposits to the place of consumption. They should not go out 
of their way unnecessarily; therefore each material should re- 
main on the straight Hne leading from its deposit to the place of 
consumption. Unless the way of one should lead by chance 
through the deposit of another, all these ways will meet for the 
first time in the place of consumption. Since their assembly at 
one place is the necessary first condition of manufacturing the 
product, the place of consumption will be the location. There- 
fore a productive enterprise using several pure materials alone 
is always located at the place of consumption. 

d) If ubiquities are added the location is bound to the place 
of consumption more firmly still. The material index, which was 
I in case c, becomes less than i. The component of the place 
of consumption is not merely just as strong as all the other com- 
ponents together; it is stronger. That being true, it is quite im- 64 
possible to separate the location from the place of consumption. 

3. Use of weight-losing materials alone or in connection 
with other materials. — (a) One weight-losing material alone 
gives us again the one straight line to which the locational figure 
shrinks. But in this case the location is not mobile, for the com- 
ponent of the material deposit affecting location is larger by the 
loss in weight of the material. The material index is by this loss 
lin weight larger than i. Therefore the location is at the deposit. 

b) But if ubiquities are added, they strengthen the compon- 
ent of the place of consumption and the choice of the location 
depends upon the degree to which they do this. The location 
^remains at the deposit as long as the material component remains 
larger, i.e., as long as the material index remains larger than i. 


As soon as the component of the place of consumption exceeds 
in weight (i.e., as soon as the material index becomes less than 
I ) , the location moves to the place of consumption. Therefore 
the choice of the location is determined by the comparative size 
of the losses in weight and of the weight of the ubiquities. 

c) Several weight-losing materials alone make impossible a 
precise single statement concerning the position of the location. 
In such a case the locational figures of our theory become oper- 
ative. The general theorems we have obtained allow us to say: 
If weight-losing materials alone enter into the production, the 

.— _p, 

material index is always more than i, and the location of pro- 
duction will therefore be drawn somehow towards the material 
deposits. From our mathematical analysis we know by what 
arcs running through the material deposits the location is deter- 
mined in the case of two materials. We know further that the 
location can lie at the place of consumption only if the latter lies 
by chance within this arc; and that the location goes in every 
instance (when two or more materials exist) entirely to one de- 
posit, if the weight of this one deposit is equal to that of all the 
rest of the deposits plus the weight of the product. This latter 
fact enables us to realize in what case coal, for example, has the 
power to attract the location to its deposits ; it is the case when 
its weight is equal to the weight of the product plus that of all 
65 other localized materials employed. 

If more than two materials enter, Varignon's frame may be 
used, as we know. We may visualize the geographical region at- 
tracting the location which is created by the preponderance of 



the material index more distinctly by connecting the points of 
material deposits into one figure (Cf. Fig. 9). The triangle Mi, 
Mo, Ms will be the region attracting the location. Its force of at- 
traction will be greater to the degree that the preponderance of 
the material index is greater. 

d) Weight-losing materials together with pure materials 
cause the material index to become smaller, since the pure mate- 
rials appear again with their entire weight in the component of 
consumption. Therefore the tendency toward the material de- 
posits will be lessened. In this case also the location can never be 
at the place of consumption unless the component of consump- 
tion is strengthened by ubiquities. On the contrary, it will al- 
ways be situated near the deposits unless the place of consump- 
tion should accidentally lie upon the appropriate arcs. The 
deposits of pure material have no attracting force, however. 
Therefore the figure of the weight-losing materials (Fig. 9) can 
be used again to see where the geographical center of attraction 
of the location lies and how strongly it pulls.^ 

^ This does not seem correct in view of what has gone just before. To be 
sure, the deposits of pure material would not exert the same kind of influence as 
the weight-losing materials. But suppose the proportion of weight of the pure 
materials were considerable in the particular product and they happened to He 
between the deposits of weight-losing materials and the place of consumption, 
hke this : 

Ai Bi Ai and A2 are the deposits of the weight- 

losing materials ai and ao', 
. C Bi and B2 are the deposits of the pure 
A2 Bi materials bx and bz. 

Obviously, if the weight-losing materials alone determined the location of the pro- 
luction, it would probably be at the point halfway between Ai and A2 if we as- 
sume tti and 02 to be of equal weight as well as of equal weight loss. But this 
would mean that bi and 62 would have to be transported all the way back to that 
ooint. Obviously, then, the place of production would lie somewhere upon the Hne 
connecting C with the point halfway between Ax and A2. This point would be 
-vhere the sum of the ton-miles of weight losses fli, 02 would be equal to the sum 
)f the ton-miles of bi, bt. — Editor. 


e) If, finally, ubiquities are added also the locational effect 
should be clear from what has been discussed without further 
explanation. The material index will decrease exactly in propor- 
tion to the extent of their use, and the influence resulting from 
the loss in weight of the other materials will be counterbalanced. 
As soon as the losses in weight are actually balanced by the 
weight of ubiquities, the material index becomes equal to one and 
the location lies at the place of consumption in spite of the losses 
in weight. Exactly to the extent to which this condition is ap- 
proximated as a result of adding ubiquities, the attracting force 
of the figure of the material deposits will decrease and the at- 
66 tracting force of the place of consumption will increase. If we 
wish to know whether a productive enterprise using all these 
different kinds of materials is attracted toward the material de- 
posits or toward the place of consumption, we have to compare 
only the loss in weight of its localized materials with the weight 
of the ubiquities which it uses. Accordmg to which weight is thej 
greater, one or the other attractive force is greater. 

All this may serve to make concrete the mathematical theory i 
and to show how it operates when it is applied to individual in-' 
stances and to show that it covers them. Our construction (or,j 
if the figure becomes too complicated, Varignon's ''frame")! 
affords us means of determining exactly the location in every 
individual case. As the foregoing examination of individual 
cases has shown, this construction and frame are, however, nec- 
essary only when weight-losing materials are used, because only 
in this case do we get locational figures in which the location does 
not lie at the place of consumption. In all other cases it is at thej 
place of consumption except: (a) when only one pure materialj 
is used; in that case the location is mobile along the way between 
the material deposit and the place of consumption; (b) wherj 
only one weight-losing material is used; in that case the locatior 
lies at the material deposit; (c) when ubiquities are used in ad^ 
dition to a weight-losing material; in that case the location liesj 



either at the deposit or at the place of consumption, depending 
upon the relationship between loss in weight and the weight of 
the ubiquities. 

All this follows from applying the general mathematical 
theory of minimum points to the combination of facts which the 
various industries present. 


Up to this time we have confined our analysis to examples of 
the transport orientation within isolated or single locational fig- 
ures. But it is evident that fundamentally the same reasoning 
applies in the case of the orientation of an entire industry. For 
after all this orientation means, as far as transport orientation is 
concerned, simply the co-existence of a larger or smaller number 
of independent locational figures which are formed by the vari- 
ous places of consumption and the material deposit. Still, it is 67 
well to take up a few more questions. 

A. First of all. How do we get the locational figures appro- 
priate to the orientation of an entire industry? Which are the 
most favorably located deposits for each place of consumption? 
Are they simply and in every case those geographically nearest 
each place of consumption? 

They are in fact the geographically nearest deposits, assum- 
ing a simple condition in which no complicated locational figures 
3f counteracting forces are created. If only one material is used 
t is self-evident that the nearest deposit will be chosen, whether 
:he place of production lies at the deposit, along the line between 
he deposit and the place of consumption, or at the place of con- 
sumption. It is self-evident also that the nearest deposit will be 
ised if several pure materials are employed either alone or in 
:onnection with ubiquities, because the location will lie at the 
)lace of consumption, and using the nearest deposit will facilitate 
)ringing the non-ubiquitous materials to the location. And final- 
y, it is self-evident that likewise the geographically nearest de- 


posit will be chosen if weight-losing material is combined with 
other materials without the existence of a complicated locational 
figure — in other words, when ubiquities are added to only one 
such material. As we know, the location in this case may be 
either at the deposit of that material or at the place of con- 

But in the case of an actual locational figure, the deposits 
which form the figure need not necessarily be the deposits geo- 
graphically nearest to the place of consumption. The following 
may serve as an example : Let us assume that GM is the deposit 



of weight-losing material in a wide territory and without compe- 
tition. Two deposits of pure material, however, compete with 
each other, and of these RMx is nearest to the place of consump- 
tion, but farther from GM than is RMo, as the figure shows. Let 
the location be near GM on account of the preponderance of the 
68 loss in weight. It is evident that not RM^, the deposit nearest 
geographically to the place of consumption, but RMo, the deposit 
nearest geographically to GM, will be used in the productive 
process and will therefore form the "figure." Obviously, if thd 
location lies near GM, pure material obtained from RM^ wouldi 
have to make a long trip first down to GM and then back again! 
to the place of consumption; while this trip is saved if RM2 is 

Stated generally, this means that the factor which deter-i 


mines whether a given deposit will be used in forming the loca- 
tional figures is the index of transportation costs of the figure 
thus resulting. The figure which has the lowest index of trans- 
portation costs triumphs in the competitive struggle, and for 
that reason is to be looked upon theoretically as the one really 
applicable. Thus the deposit that will be utilized is possibly not 
at all the one of its kind geographically nearest to the place of 
consumption. If the location does not lie in the vicinity of the 
place of consumption, but rather in the vicinity of a deposit 
(i.e., if the materials, or indeed one of them, predominates), 
geographical proximity to the place of consumption will be de- 
cisive only in the case of this one material. But in the case of 
the other materials, proximity to the deposit of the predomi- 
nating material will be the significant factor in determining 
which particular deposits will be used in the productive process, 
and will in consequence determine the locational figure. In those 
modern industries, for example, in which coal represents such a 
predominating material, the geographical proximity to coal de- 
posits, and not to places of consumption,. decides whether par- 
ticular deposits of the remaining materials will be utihzed. To 
be sure, in these instances the production will be oriented in lo- 
cational figures which are formed by coal deposits, which are in 
geographical proximity to the respective places of consumption; 
but this having been taken into account, the locational figures 
are formed by the material deposits which are as near as pos- 
sible these coal deposits. Such figures therefore have a narrow 
base at the coal deposits and a long point extending to the places 
of consumption. Material deposits lying very near the places of 69 
consumption but far from the coal deposits remain unused. 

It should be clear theoretically now how these locational fig- 
ures are created when numerous deposits are available — as is 
true in practical Hfe. The exact mathematical method to be used 
in determining these figures in case the optimal deposit of one 


material is definite and a second material is then introduced is 
offered by Mathematical Appendix I, §io, Fig. 52. 

In Fig. 52 ^1 is the place of consumption, A 2 the deposit of 
the one predominating material whose deposit is definite, A-^ 
(which is assumed to be mobile) representing the still undeter- 
mined deposit of the second material. The lines of equal trans- 
portation costs, which are drawn for the location figures arising \ 
fiom various possible positions of A 5, indicate which of the sev- 
eral deposits of the second material will actually be used for the 
locational figure. Naturally that deposit will be chosen whose 
use entails the smallest transportation costs. This will be the de- 
posit within the lowest lines of transportation costs as drawn in - 

Fig. 52. 

B. Two more aspects of the orientation of an entire industry 
should be mentioned : 

a) It is not necessarily the case that but one single place of I 
production exists for the supply of every place of consumption. 
Firstly, it can and will happen that several locational figures 
with equal or approximately equal transportation cost indices 
exist. If, for example, one material lies nearer the place of con- 
sumption in one locational figure while the other material lies 
nearer the place of consumption in the other locational figure, 
the two figures have equal transportation costs indices. This re- 
sults in equality of competition and makes possible the use of 
the places of production of both figures. This might be the out- 
grov/th of natural conditions ; but it may also happen that an ap-i 
propriate tariff policy might equalize the transportation costs 
indices. Secondly, and more important still, it can and will hap- 
pen that the normal output of the material deposits of the most 
favorable locational figures may not be sufficient to supply tho 
70 demand of the place of consumption. In that case less favorable 
locational figures appertaining to the use of other material de- 
posits will of course be brought into play. As a result large cen- 
ters of consumption (especially the modern metropolis) will 


often be supplied by a multitude of places of production which 
belong to locational figures with different transportation cost in- 
dices. These places will, as they grow, continuously bring to 
life ''dead material deposits," and they will bring into existence 
new locational figures whose place of consumption they repre- 
sent. As a result they will create new places of production. 

b) Just as the possible output of a material deposit may be 
smaller than is necessary for the supply of the place of consumjv 
tion to which it belongs locationally, so the possible output may 

Fig. II 

be greater, very much greater. That will be the case for all ma- 
terials localized in large masses. The result is that such a mate- 
rial deposit is used, not only for that first place of consumption, 
i but also for all other places of consumption for which it gives 
' better transportation cost indices than do other deposits. Such 
material deposits will accordingly appear as the center of loca- 
I tional figures grouped about them. If they quite definitely pre- 
, dominate in attracting the location, these deposits will become 
! the center of a production whose products are distributed in all 
directions. All this should give a sufficiently clear idea of the 
orientation of an entire industry so far as transportation costs 
are concerned, not merely an idea of the orientation of an indi- 
vidual plant. Of course, this is only a theoretical statement; how 
the orientation of industry will look in actual cases cannot be 
stated abstractly. The factors, however, upon which the orienta- 


tion of an industry depends calls for a discussion with a view to 
determining how they change under the influence of the actual 
71 development of the economic system. 


Theoretically speaking, the only factor upon which the 
choice of the location of an industry depends, so far as transpor- 
tation is concerned, is the material index of the industry and the 
composition of that index. The fact should be emphasized that 
nothing else can determine or change the fundamental transpor- 
tational network of orientation except this factor; and this fac- 
tor is determined wholly and exclusively by the temporary tech- 
nical situation in the various branches of production. We shall 
see later how the extent of the deviations from this fundamental 
network (deviations produced by other causes or factors of ori- 
entation) is determined: first, by further factors related to the 
nature of the various branches of production; second, by gen- 
eral environmental conditions, such as the ''density of consump- 
tion," the resulting "density of production" and the existing gen- 
eral "rate level" of transportation. In molding the fundamental 
transportational network of industrial orientation these factors 
amount to nothing. The increasing "density of consumption" 
may necessitate the utilization of new material deposits because 
of the insufficiency of those already used ; it may thereby bring 
into existence further locational figures and places of produc- 
tion, and thus cause a further evolution of the fundamental net- 
work. But the rise or decline of the general "rate level" does 
not change anything at all in the whole picture. It does increase 
or decrease the "cost index" in all locational figures, but it dis- 
places thereby neither the location within these figures nor the 
interacting conditions of their formation. Paradoxically, the 
fundamental network of the orientation of industry, which one 
thinks of as being under the exclusive influence of costs of trans- 
portation, is independent of the general level of these costs. 


In fact, however, the transportational orientation of indus- 
try which seems so exclusively determined by the relations of 
materials depends, on account of these relations, upon two fac- 
tors. These two factors determine the "material index" of every 
I industry (which is, as we have seen, the theoretical expression of 
1 the determining relations of the materials). One is the size of 
the weight losses of localized materials during the process of 
production, and the other is the weight of the ubiquities used. 72 
' Every increase of the weight losses in production increases the 
material index; and every increase of the use of ubiquities de- 
creases it, and vice versa. And it is important to observe that 
these are the 07tly two things which are able to increase or de- 
crease the material index; they therefore determine it and thus 
settle the question (which depends upon the material index) 
whether an industry is more attracted toward materials or to- 
ward consumption. In any given industrial process it is the pro- 
portion of the weight of the ubiquities used to the weight losses 
of localized materials which gives the basic answer to the ques- 
tion whether the particular industry settles at the places of con- 
sumption or moves to the material deposits. 


What significance has the foregoing statement for the devel- 
opment of transport orientation? How do these two conditions 
change in it, and with what result? This is the situation: In 
reaHty, development generally means in good times a continual- 
ly increasing control of nature and a continually progressing 
concentration of population. Development, thus defined, pro- 
duces the following changes in the conditions of transport orien- 
tation : 

In the first place, the development will, as it concentrates 
population, produce an ever-increasing demand for the available 
amount of ubiquities. In consequence, unreproducible ubiqui- 
ties will be used up at certain places, and reproducible ubiquities 


will be in such demand at many places that the demand will ex- 
ceed the local output. In both instances this will eliminate the 
ubiquities from the production at these places; in the first in- 
stance entirely, and in the second instance for that part of the 
production whose demand can no longer be supplied locally. 
And this elimination of ubiquities will, with the progress of de- 
velopment and an increasing concentration of population, as- 
sume ever greater proportions. This process can, practically 
speaking, go so far in regions of concentration of population that 
73 the manufacturing of materials which might in themselves (i.e., 
technically) be producible anywhere becomes in fact a manufac- 
turing of materials which must be obtained from other places, 
(i.e., localized materials). This means that the development, in 
so far as it signifies concentration of population, continuously di- 
minishes the share of ubiquities in production and substitutes 
localized materials in their place. This constantly lowers the 
weights of the components of the place of consumption. This is 
one effect of the general development. 

In the second place, development, in so far as it signifies an 
increasing control of nature, will influence the amount of the 
losses in weight of the localized materials thus increasingly used 
in production. One could describe what takes place (on account 
of the increasing control of nature) as a continued further tran- 
sition from the use of materials which nature offers to man ready 
for use — examples being wood, clays, etc. — to the use of mate- 
rials, such as minerals, chemical substances, etc., which can be 
wrung from nature only by means of industrial processes. This 
means that increasing losses in weight will take place in produc- 
tion. For the processes which yield the new materials are ordi- 
narily burning processes, and therefore, as a result of the use of 
fuel material, they are processes of considerable weight losses. 
Moreover, the new materials themselves, because they must be 
isolated, entail heavy losses in weight and leave behind "resi- 
dues" which are on the average greater than the residues of the 


old materials like wood, clay, etc. Consequently the more such 
new materials enter into production the more losses in weight 
will be incurred by the ''materials" used in that production. Fur- 
thermore, the control of nature leads quite generally to "mech- 
anization" of production. Since this involves the use of fuel ma- 
terial, it results in transforming every mechanized process into 
a ''process of weight loss," and in generally increasing the losses 
in weight. The development thus increases greatly and in many 
ways the weight losses in production, and therefore it tremen- 
dously strengthens the material components in addition to weak- 
ening the components of the place of consumption by displacing 
the ubiquities. 74 

In consequence, industry must shift decidedly and continu- 
ally from the places of consumption toward the material de- 
posits. And in fact this view of the general development enables 
us to understand the fundamental features of the large indus- 
trial revolution which we have witnessed during the nineteenth 
century. The rapid concentration of population and the rapid 
technical development with its mechanization of production and 
its transition to the use of metal both tended to destroy (and 
just as rapidly as they took place) the condition which had pre- 
vailed up to that time, the condition that industrial location, in 
so far as it was determined by transportation, coincided with the 
places of consumption. This removal of the location of indus- 
trial production from the places of consumption implied the de- 
struction of the crafts, for the crafts presupposed that industrial 
location and the place of consumption coincided. Here we have, 
as far as locational theory is concerned, a general basis for un- 
derstanding the inevitable collapse of this kind of industrial or- 
ganization. Of course the crafts were undermined by many dif- 
ferent forces, almost all of them strong. It is certain that the 
change of locational conditions which has been pointed out was 
not the weakest of these forces. 



Let US now, for the completion of our theory, leave the ab- 
stractions with which we have been working up to this time and 
modify our conclusions in order to fit them into reality. We have 
to abandon two assumptions. The first is the assumption that 
weight and distance are the only factors that determine the costs 
of transportation. This was the fundamental assumption of our 
entire discussion; upon this theoretical basis the locational fig- 
75 ures and the positions of location were worked out. The second 
assumption was that costs of transportation, however they mayij 
be determined in individual instances, are always uniformly fori 
a whole country those of a single method of transportation. Thisi 
second assumption accompanied the first one in all our discus- 
sions. Stated positively, these two assumptions mean that in 
order to fit our theory into reahty we have to consider, first, the 
existing system of transportation rates, and second, the inter-j 
action of several transportation systems. 


We have already discussed in Section I (pp. 43 ff.) how the« 
deviations of the actual rate structure from the theoretical cal- 
culation of rates according to weight and mileage may neverthe- 
less be expressed in terms of these two elements, weight and* 
mileage. We saw that deviations which increase or decrease thet 
mileage rate (that is, deviations which produce increased or de- 
creased rates for certain kinds of way, individual lines, or cer- 
tain distances) are capable of being expressed as additions or 
subtractions of mileage. We also saw that deviations which are 
variations from the pure calculation of rates according to weight 
(that is, deviations which produce increased or decreased rates 
for certain kinds of goods) are capable of being expressed as in- 
creases or decreases in weight, as ''fictitious" additions or sub-' 
tractions of weight; this being true whether they affect the vari- 


ous kinds of goods generally, or only under certain conditions. 
That was the theoretical solution/^ 

The next question is what significance these modifications 
have for the structure of the transport orientations. How does 76 
it change the locational figures, and how does it influence the 
position of the locations in these figures? 

a) The deviations from the pure calculation of rates ac- 
cording to mileage. — If certain lines are shortened in mileage by 
special lower rates, or if long distances are shortened in general 
by means of a decreasing scale, it evidently changes the relation- 
ship of the various points to one another, as they are considered 
for the locational figures. Viewed from the places of consump- 
tion, certain material deposits may be for locational purposes 
closer or closer together than would be the case in terms of their 
actual geographical position. Viewed from the material deposits, 
a similar situation may seem to obtain. Since the distance of the 
material deposits from the places of consumption and from one 
another determines, in terms of the lowest transportation cost 
index (cf. above, p. 67), what locational figure will be created, 
these rate variations alter the competitive relationships of the 
material deposits supplying the places of consumption, and con- 
sequently the locational figures change. Certain material depos- 
its which would otherwise not be used for forming the locational 
figures of certain places of consumption will now be used; and 
Dthers, which would otherwise be used, will now be eliminated. 
En this way, in fact, entirely different locational figures and 
places of production may be created for the supply of the places 
Df consumption than those we should assume, considering mere- 
ly the geographical locations. Within the locational figures, how- 
ever, the locations of production will be determined exactly in 
iccordance with the rules previously indicated. Expressed dif- 
erently, the theoretical position of the location in relation to the 
naterial deposits and the place of consumption will not be 

'" Cf . p. 46 f., above. 


changed at all; only the locational figures within which the loca- 
tion is determined will be changed. Looking at the map, one will 
perhaps be surprised that this or that location has not used an- 
other deposit which lies nearer geographically. One will find no 
deviation, however, from the general rules determining location 
when the material deposits actually chosen are used in the cal- 
77 culations. 

b) Deviation from the pure calculation of rates according 
to weight. — Evidently the commodity which enters into the loca- 
tional balance with added or subtracted weight influences the^ 
locational balance with another than its real weight; it attracts 
the location either more or less than its real weight would enable' 
it. If a proportional addition or subtraction of weight does noti 
take place in the case of all the materials, and also of the prod- 
uct, and therefore does not alter proportionally the attracting' 
forces of all corners of the figure, a displacement of the location 
will result within the locational figure, the location being at- 
tracted in the direction of those corners which have a propor- 
tionally increased force. 

If, for example, the industrial product is bulky, such as: 
chairs, vats, or casks, and if materials used in its manufacture! 
are not as bulky, the attracting force of the component of the| 
place of consumption will be one and one-half times the weight' 
of the product, according to the German rates. The attracting 
force of the place of consumption will, in other words, be nol 
merely the sum of the weights of materials used, as the pure the^ 
ory would suggest, but one and one-half times that sum. It mayl 
thus happen that the location which, if the goods had not beeni 
bulky, would have come to lie somewhere between the material! 
deposit and the place of consumption, will lie at the place of con^i 
sumption now that the weight of the product is in effect onei 
and one-half times as large as the sum of weights of the materialjj 
This is certainly in reality not a rare occurrence in the case oi 



bulky goods. Similarly, a raw material, which is bulky (wool) 
but whose product (yarn) is not bulky, may, of course, pull the 
location to its material deposit or to the vicinity of that deposit. 
The same reasoning applies to combustible goods. 

We find a corresponding, though reverse, effect when rates 
are reduced on goods of small value per unit of weight. Such re- 
duced rates will almost always be in effect subtractions from the 
weight of materials, while they leave the products untouched ex- 
cept for occasional small reductions; for the products have a 78 
higher value than the materials. Reduced rates on goods of 
small value will therefore almost always mean reduced attract- 
ing force along the components of the material deposits as com- 
pared with that of the place of consumption, and consequently 
the location shifts toward the place of consumption. If, for ex- 
ample, in Germany almost all raw materials of very small value, 
such as clay, ore, and wood, are transported at rates reduced as 
much as 60 per cent, and coal at rates reduced 56 per cent, it 
surely means a strong tendency to shift the location away from 
the material and coal deposits toward the places of consump- 
tion." Such low rates, therefore, constitute an attempt to dis- 
tribute or decentralize the locations of production. Our theory 
explains to what extent this distributing measure will succeed, 
and to what points the locations of different industries will be 
shifted. For the locational figures we need simply to ascribe to 
such goods as are transported at reduced rates a weight which is 
reduced correspondingly. When we construct the locational fig- 
ures we can then calculate exactly where the transportation 
costs will pull the locations as simply as in the case when no such 
reductions are made. Whatever alterations are thus created by 
reducing or increasing the rates of certain types of goods, they 
constitute important but exactly determinable shiftings of the 
ocation within the locational figure. It is to be noted, however, 

" The situation in the United States is similar. — Editor. 


that this is their only effect. A change of material deposits does 
not take place, since such special rates will always affect all de- 
posits of the same material to an equal degree, but not the mile 
age. Only a change of these distances can change the competi- 
tive advantage of various deposits and thus alter their use within 
the locational figures. In distinct contrast with the first case 
(see p. 76), which changed the locational figures themselves, 
these locational figures now under consideration remain un- 
touched by rate reductions on certain goods, and untouched also 
on the whole structural foundations of the orientation of pro 
duction; only the locations themselves shift upon these founda 
79 tions. 

The increased rates for shipments in small quantities (less 
than carloads and piece-goods shipments) ought to be mentioned 
specially. These rate increases may theoretically be expressed 
as weight additions. They do not, however, concern certain defi- 
nite kinds of goods; they concern all goods, whenever shipped 
in such quantities. They seem to create no factors which can be- 
calculated precisely and generally when determining the loca 
tion, since we cannot know whether the production of a giver | 
product will or will not attain the quantity which is necessary 
for the normal rates to become effective, and whether transpor- 
tation will or will not have to take place at the increased rates 
The distortions of the ^'theoretical" locational picture which an 
thus brought about seem not to yield to general statements, al) 
though they can be calculated precisely in every individual casfj 
and for every locational figure. We may simply ignore these dis 
tortious for the present, for every locational figure has obviouslj 
a definite capacity for moving masses within it, which capacitj 
is determined by the size of its place of consumption. In one lo- 
cational figure, full carloads, in another only less than carloac 
shipments, will be moved. In the one locational figure transpor* 
tation, and therefore production and consumption, will be cheap 
er than in the other; but this will influence neither the figures 



themselves nor the position of the location within them. Accord- 
ingly this modification of the pure calculation according to 
weight may as a practical matter be omitted from our consider- 


Our theory has thus far assumed the system of transporta- 
tion to be uniform for the whole territory considered. This does 
not need to be the case; any existing system may be divided into 
independent parts. The theory has also assumed the system of 
transportation to be of one kind. This is in reality not the case; 
there are railways, waterways, and highways. In applying our 
theory to reality we are confronted with the problem of deter- 
mining the importance of these differences. 


A few words will suffice to discuss the possible division of 
the transportation system into parts which, although co-operat- 
ing technically, operate as economically independent units. If 
such division results in independent rate-making by the various 
parts (and only in such event, of course, is it important for 
transportation costs) it may be expedient to treat each region 
(with its different rates) simply as a separate territory within 
Arhich industry orients itself. The decision whether or not to do 

'^ This modification becomes important when the production of several 
. ocational figures is "coupled" by agglomeration with one another. In the result- 
ng combined figures the si2e of a single place of consumption no longer deter- 
mines the possible amount of commodities moved; and therefore the rate. The 
hipping of materials to the "places of the combined production" may be done 
1 carloads and therefore at cheap rates, although the capacity of the individual 
laces of consumption only admits of shipments in smaller quantities, and there- 
Dre at higher rates. This condition will have the same effect as an "addition in 
eight" to the products, and therefore it means a strengthening of the compo- 
ents of places of consumption. It would perforce have in itself the tendency to 
lift the combined location toward the places of consumption ; if not, other shift- 
igs would take place in the case of such combined locations — all of which makes 
seem inadvisable to analyze this tendency further at this juncture (cf. injra, 
3. i34ff.). 



so will depend upon the extent of the differences in the rates. It 
would be expedient to do so, for example, when very many addi- 
tions and subtractions from the normal rates are made in the dif- 
ferent regions. In this case a considerably different "theoretical" 
distinction of the locations would prevail in each of the regions, 
and it would be better, therefore, to consider them independ- 

On the other hand, we may treat the rate variations as local 
modifications of a uniform system of rate-making in a uniform 
territory of orientation. To do so will be possible and expedient I 
only when nothing but the rates of some unimportant goods vary- 
from one territory to another. This situation exists, for example, 
with regard to the system of rates within the German Common- 
wealth, and this fact makes it possible for us to treat the entire 
German territory as uniform, as far as the orientation of indus- 
try is concerned. 


When different kinds of transportation systems work to- 
gether, more complicated problems seem to confront us. Bui 
they only seem to do so. If we consider the situation as it is to- 
day the problems may be solved. 

If we look at the railway system, it appears to be a net which 
may be illustrated by the diagram in Figure 13. Within thisi 
net the existing places of consumption and the deposits of mate) 
rial are located at certain points as indicated in the diagram j 
This net has been created in order to connect these centers witij 
one another. It connects them, however, not by straight lines 
but by lines having many curves, the curves being caused by thc( 
presence of other centers and by geographical conditions. Th<i 
relation of the mathematically straight connections of the idea 
locational figures to the actual connections may be somewha 
like those indicated in the diagram. The actual transportatioi 
depends upon the actual connections, although it may be pos^ 


sible to suggest, and even to bring about, certain improvements 
in the actual connections as a result of studying the require- 
ments of the locational figures. Anyway, the mathematical lines 
connecting the deposits of material with the place of production 
and the latter with the place of consumption will in a real case 
appear only as curves; that is self-evident. Has that fact any 
significance for the application of our rules? The answer is: 

Fig. 13 

Yes, in so far as the choice of a location can only be an approx- 
imation of the ideal location because the actual location is im- 
bedded into a curved network of transportation. Among the lo- 82 
cational points which may in fact be considered in view of the 
presence of the network of transportation, that point will be 
:hosen which corresponds most closely to the conditions of the 
ideal location. As is indicated in the diagram, several of the 
ictual points near the ideal location may be considered. One of 
hem, however (P'), will be chosen; because it, although lying 
geographically farther away from the ideal point, corresponds 
oest with the ideal requirements so far as its position in relation 
the material deposits and the place of consumption is con- 

Having set forth this "deforming" effect of reality, we shall 
)roceed to examine how several kinds of transportation systems 
v^ork together. 


a) The effect of the waterways. — Today railways and high- 
ways work together. If we treat the railway system as the nor- 
mal system from which we start in our analysis, we find water- 
ways a somewhat cheaper system and highways a considerably 
dearer system. What, with reference to location, is the signif- 
icance of competing waterways whose rates are today in Ger- 
many something like half the lowest railway rates, or about 0.25 
cents per ton-mile? Let us reflect how waterways and railways 
are related today geographically. Ever3rwhere we find an ex- 
tremely dense railway net spanning the entire country, and wind- 
ing through this net like ribbons, some natural or artificial wa- 
terways. These may be connected so as to form a ''network" ori 
they may be large unconnected rivers. But even in the case of a; 
network they form a skeleton of such irregularity that they can- 
not open up all material deposits of the country, and even less; 
can they supply all its places of consumption. As transportation! 
devices connecting cheaply only certain points, they thus tra- 
verse the railway system which does open up all material de- 
posits and does supply all places of consumption, and therefore 
actually carries the orientation of industry. Along the railways 
the largest part of the places of production and of the materia»! 
^2> deposits of the country are situated. The railway net contaimi 
therefore the attracting points upon which the locational figure«! 
and the fundamental outline of the orientation of industry de j 
pend. The waterways which traverse the railway system are i 
effect nothing but routes with especially cheap shipping oppoi 
tunities; they may and will be considered as parts of the railwaj 
system with especially low rates. Thus they are theoretical!) 
fitted into the concept of a single and uniform system of trans 
portation, and consequently into our theory. For within such i 
system, routes with cheaper rates mean nothing but distanceii 
shortened in proportion to the decrease in rates. In forming thfj 
locational figures, material deposits which can use these short' 
ened routes will have an advantage over other deposits whicl- 




cannot use them. The sphere of action of certain material de- 
posits will be enlarged; other deposits will be eliminated; and 
certain locations will be transferred: these are the effects of the 
competition of waterways with railways. If we know the rates 
of existing waterways under discussion it is not difficult to put 
them as locational elements into our analysis and to determine 
the resulting locational figure according to our rules. We can 


Fig. 14 

Fig. 15 

make clear their influence by the diagrams as shown in Figures 
14 and 15. 

Case I : Elimination of a deposit of material and addition 
of another through the influence of a waterway, transfer of the 
locational figure and of the location (compare Fig. 14). 

The deposit M2 is considerably nearer the place of consump- 
tion C than the deposit M\. If no waterway existed, the loca- 
tional triangle with the place of production P would be formed 
for the supply of C. The existence of the waterway may, how- 
ever, cause the distance separating M'2 from C to become eco- 
lomically shorter than the distance separating M2 from C. In 84 
hat case the locational triangle using M\ and the place of pro- 
iuction P' will come into effect. 



Case 2 : Naturally, the effect is not necessarily so far-reach- 
ing; it is possible that no change in the utilization of the mate- 
rial deposits is brought about. In that case the locational figure 
remains the same, and only a displacement of the place of pro- 
duction takes place. Figure 15 will illustrate this smaller effect. 

Here also Mo lies nearer the place of consumption than M\, 
but the locational triangle M^M^C permits the use of the wa- 
terway. The location P' (which was chosen with a view to using 
this waterway) should therefore have a smaller index of trans- 
85 portation costs than the location in the triangle MxM'o C. There- 
fore Mo will not be eliminated, and the locational triangle with 
the material deposits it employed will remain the same as if 
there were no waterway. However, the location will be reahzed 
in P', and not in P, which is the most desirable location if merely 
roads are used. 

These remarks will suffice to make clear the greater or lessi 
effect of the waterways, and at the same time to show why thai 
waterways are fringed with places of industrial production. Allj 
these locations have, during the process of their becoming estabn 
Hshed, received a little jolt from the waterways which pushed 
their position to the right or to the left. Although they now have 
their chimneys smoking by the water side, they belonged some 
where in the "neighborhood," even if there had been only trans- 
portation by land. 

b) The effect of the net of highways. — It is well known thai 
the costs of transportation on the highway are on the average 
four to ten times, and in individual cases twenty times, those of 
the railway.^^ As a result, freight transportation on the high^ 
ways over long distances has ceased. Today highways are used 
only for transporting goods to and from the railway stations^ 
Consequently highways no longer have any independent loca- 

" These sentences were written before the advent of the truck, but the stUn 
dent of this treatise will find it possible to work out the problems created by it 
if he will use the methods set forth herein. — Editor. 


tional signficance at all; their function is rather that of a sub- 
sidiary of the railway system. If we wish to understand the im- 
portance of this subsidiary, we had best consider each district of 
collection and distribution grouped around a railway station as 
a unit with the railway station as its center. As such a unit the 
district, whether a material deposit or a place of consumption, 
enters into the total industrial orientation through its railway 
station. We can disregard for the moment how the district is or- 
ganized internally under the influence of its street system; this 
is a locational problem similar to that which asks how industry 
is grouped in a metropolis under the influence of the traffic fac- 
tors present there; it is a question of local agglomeration and 
distribution which will be treated in a later chapter. If such a 86 
railway station unit (Bahnplatzeinheit) , as I should like to call 
it, enters as a material deposit into the industrial orientation, 
then not the price at the deposit, but the price at the railway sta- 
tion, must be regarded as the delivery price of the materials 
(price at the deposit plus freight charges of road carriage) . For 
obviously it is only on the basis of this price that the material 
deposit enters effectively into the orientation of industry. 

The particular significance of differences in the delivery 
prices will be discussed in the next section. It may be, of course, 
(and very often is the case) that the material deposit and the 
place of consumption are so situated that they do not at all need 
the railway, since they are in the same ''railway station unit." 
This means, for the orientation of industry at large, that they 
are located at the same place, and therefore do not come within 
the scope of our broader theoretical considerations. However, 
for the local orientation within the railway station unit, with its 
street net system, exactly the same rules of orientation will be 
operative in detail which determine the orientation at large for 
the whole country, with its extensive transportation system. 
Everything will simply be repeated in miniature. 




It has become possible now, in closing, to abandon several 
other important simplifying assumptions and to consider the im- 
portance of certain peculiarities of reality which have been 
ignored until now. These are, first, the price differences of the 
materials caused by the local position of the material deposits 
and the railway stations; and second, the effect of water power 
87 upon the process of production. We had said that price differ- 
ences of the materials (which price differences ordinarily would 
be an independent regional factor of orientation) may be ex- 
pressed theoretically as differences of transportation costs of the 
materials, and thus may be fitted into theory. We had said, too, 
that water power may be theoretically considered to be a cheap 
fuel; therefore it may be expressed in price differences of the 
material, and thus likewise be fitted into the theory. Some very 
important peculiarities appear, however, when water power en- 
ters in. Also the way in which differences in the prices of mate- 
rials may be expressed as differences in the transportation costs, 
and the way in which they then affect orientation, need further 
exemplification. In this exemplification we shall employ the lo- 
cational rules which we have already discovered. 


It does not concern us here from what cause price differences 
of the materials result; they may be due to differences in the 
costs of production, or due to artificial price fixing, or due to dif- 
ferences in the cost of transporting the goods to the point where 
the materials enter the larger traffic (i.e., traffic by rail or by 
water). We shall consider this point as the ''deposit" to be used 
in analyzing the large locational system, and we shall calculate 
upon the basis of the price at this point. 

Price differences themselves never change the location with- 
in the locational figure fundamentally; they merely shift the 
competitive conditions among material deposits which are equal 


in other respects. Material deposits with low prices will simply 
have larger spheres of action than appears from the geographical 
situation itself; they, rather than deposits more favorably situ- 
ated geographically, will be used to supply certain places of con- 
sumption. In brief, they will operate in the same way as the 88 
change of competition of material deposits caused by cheap 
rates for certain Hues which was discussed earlier. 


Water power may be used today as a source of power for 
production in two different forms: directly, under waterfalls, or 
indirectly, through electrical transmission. Both cases, as for- 
mer discussions have already shown, are to be treated theoreti- 
cally as fuel deposits with definite, and on the whole with lower, 
prices. The horse-power which they produce may easily be cal- 
culated in equivalent quantities of coal, and we may then com- 
pare the weight of this "white" coal and its price with the quan- 
tities of ''black" coal which it replaces. This point is simple. 
There exist, however, peculiarities in the locational effect of 
these calculated amounts of coal which have to be considered 

a) In the case of the use of waterfalls, the calculated 
amounts of coal can be used only at one place, at the waterfall. 
Locationally, such waterfalls exert an alternative locational ef- 
fect; either the location goes to the place of this locational ad- 
vantage, or it remains where it is, and in that event it is abso- 
lutely untouched by this locational advantage. When does the 
one thing take place, and when the other? If nowadays the lo- 
cations remain untouched by this locational advantage it means, 
practically speaking, the forming of locational figures and the 
selecting of locations in terms of the most advantageously locat- 
ed coal deposits. We know the locational figures thus created 
and shall consider them as normal. The use of waterfalls elimi- 
nates the use of coal deposits and involves the formation of new 



locational figures using places with waterfalls. But this means 
that the locations in the new figures are transferred to a point 
which may be theoretically new, namely, to the waterfalls. What 
is theoretically new (as compared with simply eliminating cer- 
tain deposits of coal by using cheaper or otherwise more advan- 
89 tageous deposits) is the fact that a fundamental transfer of the 
location in the figure takes place on account of the necessity of 
having the location at the place of the waterfalls. Therefore in 
all cases in which the location in the old figures was not at the 
deposit of the power material, fuel, it will be forced to go to the 
deposit of the new power material, the waterfalls. From this it 
follows, formulating our conclusions tentatively, that the loca- 
tional effect of waterfalls at which power is cheaper and better 
located than the available deposits of coal will not be as great as 
if this water power were deposits of coal offering equal advan- 
tage. For the effect of waterfalls producing water power is les- 
sened by additional costs of transportation which result when 
the location deviates from its normal point of minimum trans- 
portation costs. The locational revolution, therefore, which will 
be caused by water power, at the falls will be less than if this 
water power were correspondingly cheap coal-power. Its influ- 
ence will remain less to the extent to which the impossibility of 
transporting water power at falls necessitates a transfer of the 
location within the figure. This transfer will be most extensive in 
those cases in which the former location was least influenced by 
the component of the power deposit. 

When will the water power of waterfalls be able to super- 
sede coal deposits and to draw the location to itself? Evidently 
whenever the cost of power saved is greater than the cost of in- 
creased transportation. We shall have to compare, therefore, the 
relation between the cost of power at its location and the cost of 
coal at its deposit with the relation between the index of trans- 
portation costs of the old and that of the new location. If the 
sum of the cost of water power and of transportation to the 


water power location is smaller than the sum of costs of coal and 
of transportation to the coal location, then the water power is 
cheaper and supersedes the coal. 90 

To give an example, in Figure 16, P is the old location with- 
in the locational figure M^MoC using coal (coal at M2); W 
(waterfall) is the new location in the locational figure M2WC 
using water power. We shall have to compare the price of power 
per unit of product in W plus the index of the transportation 
costs of W {a'b') with the price (in M2) of coal used per unit of 


product plus the index of the transportation costs of P (a, b, c). 
If the former sum is smaller, the location W supersedes P, other- 
wise not. This shows that the influence of non-transmittable 
water power is rather easy to calculate. Its influence is con- 
firmed within the narrow limits which are set by the relation- 
ships of cost just discussed. Unless the distances involved are 
small, the influence of waterfalls will operate most directly in the 
case of industries which are located at their coal deposits, be- 
cause in this case the location does not have to shift within the 

b) Transmissible water power. — First, we shall as before 
substitute theoretically the amount of coal ordinarily used in 
producing i H.P. for the electrical H.P. here used. The price of 
this calculated amount of coal (at the water power location) is 
to be compared with the price of the necessary coal at the coal 

^*As it had to in the above example where the location had to go from a 
point between the deposit of coal and the deposit of the other material to the 
water power substituted for the coal deposit. — Editor. 


deposit. Thus we have expressed theoretically the power uti- 
lized in terms of a hypothetical coal deposit which would have a 
definite, and probably on the whole, a lower, price. Second, we 
shall consider the cost of transmitting the H.P. used as if it were 
the cost of transporting the calculated amount of coal. On the 
whole, we shall find that locations of water power which have 
good electrical transmission yield an exceptionally low price for 
the power as calculated in terms of coal, and exceptionally low 
91 rates of transportation per ton-mile. The effect seems clear in 
this case of transmissible water-power, for it theoretically repre- 
sents deposits of especially low-priced coal which may be trans- 
ported at exceptionally low rates. The very low price of such 
water power will, in accordance with our previous discussions, 
cause its use to a larger extent than its geographical location 
would lead one to anticipate, and will eliminate as "locational 
comers" the use of coal deposits more favorably located geo- 
graphically. The low ton-mile rates of such water power, as cal- 
culated in terms of coal, may be expressed in theoretical weight 
deductions of this ''theoretical" coal. They will shift the loca- 
tion in the appropriate locational figures toward the other loca- 
tional corners — the places of consumption and the other mate- 
rial deposits — much further than would have been the case in 
the locational figures formed by the eliminated coal deposits. 
As in the cases when non-transmissible water power was used, 
we find : ( i ) The formation of new locational figures results from 
the use of water power; and (2) a transfer of the location takes : 
place within these figures according to theoretical principles.. 
The situation differs from the previous case, however, because] 
the location is not shifting toward the power material deposit^ 
but rather in the opposite direction — that is, toward the placesi 
of consumption and toward the other material deposits. The! 
transfer of the location within the new locational figures is, how- 
ever, due to the easy transportation of the new power materials,j 
and not to their immovability. 


From these observations we may deduce the great and essen- 
tial difference between transmissible and non-transmissible wa- 
, ter power. While in the case of non-transmissible water power 
the transfer of the location from the point of minimum costs of 
transportation raises the index of transportation costs, and there- 
by narrows the ^'sphere of influence" of such places of water 
power, in the case of transmissible water power the low cost of 
transporting the equivalent of i H.P. gives additional momen- 
tum to the expansion of the sphere of influence already extended 
by the low cost of production. For it is quite obvious that the 92 

low rates for transporting electrical current (low ton-mile rates 
of the ''theoretical" coal) mean a lower index of transportation 
costs of the respective figures, and thereby put these locational 
figures on a basis which permits them to compete with other 
locational figures. If the H.P. can be produced and transmitted 
sufficiently cheaply, favorably located water power will cause a 
great number of locational figures based on coal to be eliminat- 
ed, and just as many locations to be shifted. On the other hand, 
even unfavorably located water power will not necessarily be ex- 
cluded from becoming the basis of location and production. 

We shall be able to determine, according to our theory, ex- 
actly to what extent and with what locational results these stores 
of water power will enter into modern economic life. Using the 
diagram of the last example, the location P' (based upon the 
water power in W instead of the coal deposit M2) will not be lo- 
cated at W (as in the case of non-transmissible water power), 
but in the new locational figure MJVC, and will be nearer M^ 


and C than the former location P, based upon coal in the figure 
Mil/oC. Its position within the new figure is determined by the _ 
laws which we now know so well from the previous discussions. 
The weight which has to be applied on the component WP' ob-< 
viously is the difference between the weight of the "theoretical" 
coal (water power calculated in terms of coal) which is brought 
from W and the weight deduction which has to be made along 
this line corresponding to the lower rate per ton-mile. In order 
to determine whether the location P' is possible and M. should! 
be eliminated, we shall have to add the price of the ''theoretical 
coal" (water power in terms of coal) to the index of the trans- 
portation costs of the location P\ This sum has to be compared 
with the sum of the index of transportation costs of the old loca- 
tion P and the price of actual coal per unit of product (at M2) 

93 If the first sum is smaller, P' is possible; otherwise not. This ex- 
ample is apparently capable of general application. The possi- 
bility, then, of fitting water power and its effect into the theory 
of the transportation orientation is obvious. We may well sa>| 
that we have succeeded in applying our theory to all modifica 

94 tions of complete modern reality. 





I The labor costs of an industry (in the sense in which we de- 
fined this concept in the preliminary analysis of the locational 
factors) are, in general economic terms, the expenditures of hu- 
man labor incurred in carrying out the particular process of 
production. They appear in the capitalistic system as wages and 
salaries which are paid out in the course of the productive proc- 
ess, and denote the "equivalent" of the labor used. It is obvious, 
of course, that human labor is not paid for with "wages," be- 
cause it is something different from a "commodity." However, 
the economic expression of the energies expended in labor (that 
is, the "cost of labor" of which we are now speaking) are in the 
capitalistic economy of today the wages and salaries which are 
paid out per unit of product. And since we always deal with 
economic phenomena in their concrete present form — for only 
thus do they become comprehensible — we shall in our further 
discussion deal with this sort of wages and salaries, calculated 
for the "unit of weight" of the product of our previous theoreti- 
:al discussion. 

These labor costs can only become factors in location by 
/arying from place to place. That is self-evident. But it is im- 
portant to reaHze that, since we are still investigating the re- 
gional distribution of industry, such local differences of labor 
:osts concern us only in so far as they are of significance for this 
)roblem. This means that they concern us only if in some man- 95 
ler they are connected in fact with geographically defined points, 
»ecause only in that event can they attract industry to particu- 



lar geographical points and thus have an effect on the fundamen 
tal regional distribution of industry. Only a part of the actual 
local differences in labor costs possesses that sort of peculiar ge 
ographical relationship. The labor costs of an industry may 
differ, speaking generally, on account of two quite different sets 
of causes: (i) because of differing levels of efficiency and of 
wages of labor, i.e., for more or less subjective reasons; and (2) 
because of differing levels of efficiency in the organization and 
the technical equipment with which the laboring force is set to 
work, i.e., for more or less objective reasons. However, only lo 
cal differences resulting from subjective reasons have the req 
uisite peculiar geographical relationship — are geographically 
''fixed." They are fixed differences in so far as they are a func- 
tion of a given geographical distribution of population, which 
shows different levels of wages and of performance in its various 
parts. On the other hand, the differences of labor costs on ac- 
count of different levels of efficiency of the ''apparatus" are, i1 
seems, no more geographically determined than is the use of the 
apparatus itself. These latter differences may become a factpi 
determining location in a manner that is to be taken up later ir 1 
the theory of agglomeration ; but at the present moment they an 
outside our discussion. 

We do not, therefore, exhaust at present the significance 
labor costs as a locational factor; for we deal only with that par | 
of the differences of labor costs which results from local differ! 
ences in the level of personal efficiency and wages of the popuj 
lation. I 

What particular circumstances caused these differences 01 
wages and efficiency and the consequent differences of laboi; 
costs is a matter of indifference to us and to the whole "pure' 
theory. Especially does it not concern us that their actual leve 
is, of course, not a phenomenon of "pure" economics, but rathei 
a changing consequence of extremely varied historical and nat 
96 ural circumstances. All this may be neglected by pure locationaj 


theory which is only concerned with investigating the funda- 
mental significance of such geographically determined differ- 
ences of labor costs. And for that purpose the actual level of 
these costs — and even whether they actually exist — is a matter 
of complete indifference. Pure theory conceives them as a ^'pos- 
sibility," and investigates the theoretical results of that possi- 

In one thing, however, we must be interested, namely, in the 
geographically essential ''form" in which these differences of 
cost appear. We must know in what general manner the labor 
costs, as determined by the different levels of wages and per- 
formance, are actually geographically distributed in a country 
at a given moment. Are the differences ''according to area," so 
that one may say this whole region operates more cheaply than 
a given other one? Or are they "according to place," so that 
they relate to particular towns, or at any rate to more or less 
concentrated districts which, in a general way, may be treated 
"as a town" (a mathematical point) without committing too 
great an error? Whether one or the other of these two possi- 
biHties is assumed will be of considerable significance for our 
discussion, which is to be carried on by means of mathematical 
aids. In the first case we shall have to deal with the mathemati- 
cal concept of the "plane"; in the second, with that of the 

If in this connection we are to approach the actual situation 
without prejudice, we must make various distinctions with re- 
gard to the kinds of differences in wage levels. 

We will at once recall certain differences in the wage level 
according to districts. The higher general level of wages in west- 
ern and southern Germany as compared with that of the eastern 
Dart may occur to us as an example. We may think of the fa- 
niliar tables of average local day wages which can be compiled 
from the sickness insurance data; we may remember that, with 
:ertain exceptions, the wage scales fall "like a staircase" from 


west to east; and that pointlike exceptions to this regional dis- 
tribution of wage levels are in general caused only by the large 
97 cities. If we think of these familiar facts, the 'Vage rate" will 
appear to us as a result of a superficial examination, as essen- 
tially differentiated ''according to area." 

And yet this picture is one of many statistical simplifications 
which we are always using, and which, though not actually; 
wrong, gives us an idea of reality dangerously inexact in detail. 

As evidence for this statement let us cite statistics of wagesi 
as given in their annual report for 190 1-2 by one of the largest 
German unions composed mainly of unskilled workers, the Cen- 
tral Union of Trade, Transport, and Traffic Laborers (i.e., jan- 
itors, packers, market workers, coachmen, cab drivers, furniture« 
movers, etc.). The figures are best for central Germany where 
the Union is most widely extended outside the large cities. The< 
average weekly wages of its members in marks show, in the small! 
district in the vicinity of the Harz Mountains, the following va^ 
riations: Nordhausen, 14.2; Sangerhausen, 12.0; Halberstadt 
15.7; for the district of the southern Thuringian Forest, alsc- 
not a large one — Sonneberg, 15.7; Suhl, 15.3; Saalfeld, 17.2; 
Erfurt, 19.3 ; Jena, 17.0; and for the region on the border of thu 
Saxon industrial area — Zeitz, 17.8; Greiz, 16.7; Plauenscheii 
Grund, 19.4. Here we have in each district differences of from 
M. 2 to M. 2.70 in the weekly wage, i.e., differences of up to 2i 
per cent in places very close together. Similar results are sef 
ever5rwhere. In two adjoining Silesian counties, those of Stric 
gau and Waldenburg, for instance, 12.9 and 15.3 are paid 
Hence we find, even for unskilled labor, wage rates differing en 
tirely "according to place," not only in the large towns whercj 
wage levels are naturally well above those in the surrounding 
country, but everywhere else, even in the small places in th4 
country itself. The difference "according to areas" is only th(i 
general average of very large local differences. 

If it is not permissible to assume a regional distribution 0: 



wage level even for that meanest category of labor which may 
most truly be spoken of as a homogeneous mass, evidently when 
we study the wage levels of skilled labor our guiding principle 
ought to be that wage levels will be distributed ''according to 
places." According to the report of the Union of Metal Workers 98 
for 1903, pattern-makers (in sand), for instance, earn for piece 
work in pfennig per hour in central Germany: in Hildesheim, 
41; Ilsenburg, 27; Thale, 39; Sangerhausen, 34; Gotha, 44 — a 
range of 1 7 pfennig, or 60 per cent, in the small districts around 
the Harz; in Zeitz, 24; in the nearby Gera, 34 — a range of 10, 
or about 30 per cent; in Bunzlau, 31 ; Hirschberg, 42 ; Schweid- 
nitz, 39 — a range of 11, or 32 per cent. According to the very 
complete and careful reports of the Wood-workers Union for 
1902, skilled wood-workers (carpenters, turners, etc.) earn on 
the average per week in mark: in Frankenhausen, 13.6; Kalbe, 
1 1.2; Sangerhausen, 16.7; Schkeudnitz, 21; Korbetha, 12; 
Naumburg, 18.7 — differences of 9.8 marks or 86 per cent per 
(Week within the small district between the Goldene Aue and El- 
ster-Saale. Similar differences appear elsewhere. The Thurin- 
^ian Forest shows the following figures: Koburg, 14.7; Weimar, 
21; Gotha, 20; Eisenach, 18.2 — in other words, differences of 
3.3 per week. 

All these are local differences in the small towns and in the 
'arming country; if we take the large cities into consideration, 
he local differences are much larger still. For pattern-makers it 
s only necessary, for instance, to extend our view from the Harz 
Magdeburg and Hanover. There we find average wages per 
lOur of 48-52 pfennig, wages approximately twice as high as 
hose of Ilsenburg in the Harz. Similarly for wood-workers, 
wcipzig with 23.7 or Halle with 22.3 have twice the wages of 
Lorbetha with 1 2 or Kalbe with 1 1 .2 . 

Therefore the wages even for unskilled labor, but much more 
or skilled labor, form today a rather mountainous terrain with 
eep gorges and relatively high peaks. So far as wages come into 


consideration we shall, even when differences of general level 
form a broad foundation for whole regions, think of variations 
from point to point. 

Now it is well known that differences of wage level do not 
give an adequate idea of the differences in the level of labor > 
costs. The parallelism between them is disturbed by differences 
99 of efficiency. There are two possible cases : A difference in effi- 
ciency conditioned by natural and cultural facts (nature of pop- 
ulation and environment) may exist at the same wage. This is a 
local difference. Also the results of the fact, well known empiri- 
cally to social psychology, that high wages and high efficiency go 
together may disturb things to a considerable extent. The latter 
theorem would mean that the rather mountainous picture of 
wage differences would be reflected as less mountainous differ- 
ences of cost of labor. It might even mean a complete smoothw» 
ing out of hills and valleys; or it might even go beyond that, sc< 
that places with high wages would be places of low labor costs 
In the empirical theory it will become evident that for indus-(| 
tries of a particular sort that may in fact often be the situa^< 
tion. At this time it is sufficient to point out that whether th 
differences of labor cost run more or less parallel to those oi 
wages, or whether on account of differences of efficiency the t 
diverge greatly, as a matter of fact today every employer 
every industry reckons (as a result of his experience) with thi: 
"local," and not with the ''regional," nature of the differences u 
the cost of labor. We have attempted to make clear the locai 
variation of these differences by citing examples of the extraordi 
narily large jumps of wage rates from place to place, and thi:i 
explains why, in the pure theory, we do not start from regionalj 
but from local, variations of labor costs. We shall not speak o 
''areas of labor cost" on different levels, but of labor locations 
with different costs. 

As has been indicated in the general introduction, it will b 
necessary for the present to disregard a number of qualitie 


which these labor locations in fact possess in order to make the 
effect of their varying levels of costs perfectly clear as a factor 
in the theory of location. We must neglect the fact that an un- 
limited supply of labor is, of course, not to be had at any of these 
locations at a given time at the cost which it offers, and that 
therefore it cannot attract unhmited numbers of industries sim- 
ply by virtue of this cost level. We must also leave out of con- 
sideration the fact that the cost level of each location is altered 
by every movement of industry, on account of the change in de- 
imand for labor which this movement causes. We must disre- loo 
, gard these things and imagine the cost levels of the locations to 
be fixed, and the labor supply available at each location to be 
unlimited; for only by so doing can we analyze clearly and to its 
i final consequences the effect which the differences of costs will 
have on the distribution of industry. Only if we conceive the at- 
tracting power of each location — which power is based upon 
these differences of cost — as freed from all limits but those of 
space, that is to say, only if we conceive it as actually unlimited, 
can we clearly trace its effect upon location. And it is necessary, 
of course, to introduce this attracting power as a fixed quantity; 
otherwise it could not be measured in mathematical terms. 
Hence we must regard the differences of cost as ''given"; and as 
given with unlimited attracting power. 

We shall leave it to empirical theory to eliminate these as- 
sumptions and to introduce into the picture the actual environ- 
ment within which these abstract laws work out, the significant 
elements of the actual environment being variability of the dif- 
ferences, and the connection of these differences with the com- 
petition among industries for what is at any given time only a 
'imited supply of labor at each location. Only through recourse 
;o such empirical analysis can the local movements of labor and 
he general changeability of the ground work of industrial labor 
:ost be taken account of and explained. 



How does this groundwork of labor cost effect the orienta- 
tion of industry by means of its locations of different labor cost 
levels? J 


Let us imagine again an isolated process of production and 
distribution with its raw material deposits and its place of con- 
sumption. The point of minimum transportation costs results 
from this locational figure and from the composition of the 
well-known material index. What significance will it have for de- 
termining whether production will really take place at this point 
that in the infinite area surrounding it there are perhaps points 
at which a ton of product can be produced with smaller labor 
1 01 costs? 

The following is at any rate clear: that every such point of» 
lower labor costs constitutes economically a center of attractioi 
which tends to draw industry away from the point of minima 
transportation cost to itself. But the attraction of such a cent« 
is essentially not an attraction of a mere approach; for an ap 
proach to the location with the lower labor costs would have n( 
advantage for the industry. Only a migrating to that place itself 
would be of use to it; hence there is here the issue of an alterna- 
tive attraction: the question is whether industry should operat 
at the point of minimum transportation costs or be moved to the 
labor location. 

Under what circumstances will industry be moved to the la- 
bor location, and when will it not? 

Every change of location away from the point of minimum^ 

^ Isodapane is a new technical term introduced by Alfred Weber. It is , 
constructed in analogy to the geographical term "isotherm." Similar words are^ 
current in scientific literature. Isodapane contains besides the well-known root 
isos, "equal," the word dapane, which means "expense," "cost." — Editor. 


transportation costs to a favorable labor location means, in terms 
of transportation, a ''deviation" which lengthens the transpor- 
tation routes and raises transportation costs above those pre- 
vailing under the most advantageous conditions. The changes of 
location can therefore take place only if the rise of cost per ton 
of product which it causes is compensated, or more than com- 
pensated, by savings of labor costs. A location can be moved 
from the point of minimum transportation costs" to a more fa- 
vorable labor location only if the savings in the cost of labor 
which this new place makes possible are larger than the addition- 
al costs of transportation which it involves. It is necessary to un- 
derstand this general theorem precisely, and to analyze its con- 

To understand precisely its theoretical significance we must 
bring it into organic connection with the general mathematical 
concepts which we have hitherto used. The means necessary for 
this task are provided by what is said in the second part of the 
appendix about curves of equal transportation cost. The discus- 
sion there starts from the assumption that any deviation from 
the transportational minimum point may take place in quite dif- 
ferent directions ; and that in any direction in which it may go 
there will be points at which the costs incurred in such deviation 
(i.e., the additional costs of transportation per ton of product 
caused by the deviation) are equally high. From this it follows 102 
that there must also be curves connecting such points of equal 
deviation costs which may be drawn around the minimum point 
at some distance, varying in accordance with the index of ma- 
j terials. These curves, curves of equally high additional cost of 
' transportation, form the conceptual connecting link between the 
transportational minimum points and the deviation points which 
represent the labor locations. We shall call them isodapanes (of 
equal cost), for brevity's sake. 

^ This point is hereafter often referred to simply as minimum point. — Editor. 


For every labor location, wherever situated, there must be 
an isodapane of the respective locational figure. This isodapane 
indicates how high the costs of deviating the industry from the 
minimum point of the locational figure to the labor location in 
question would be. 

On the other hand, some isodapane of the locational figure in 
location will correspond to the index of economies of the labor 
question in such a way that the deviation costs which it indicates 
per ton of product are exactly as large as the saving in labor 
costs per ton of product as compared with the labor costs at the 
minimum point. Hence it is apparent that, if the labor location 
lies on a lower isodapane than that just discussed, its economies 
exceed the deviation costs; if it lies on a higher one, the devia- 
tion costs exceed its economies. That means that a labor location 
will attract the industry if it lies within the area of this isoda- 
pane, because in that event its economies are greater than the 
deviation costs and the migration to it will cause greater econ- 
omy than it causes increased cost; and vice versa, it ca7inot 
attract, cannot bring about the migration of the industry if it 
lies outside of the limits of this isodapane, for in that case the 
economy is smaller than the deviation costs. With regard to the 
attracting power of this labor location, this is the critical isoda- 
pane. To every labor location, no matter where situated with 
any index of economy whatever, there must correspond such a 
103 critical isodapane. The relation of the labor location to this 
critical isodapane — whether it lies inside or outside of it — de- 
termines whether or not such a location will attract the produc- 
tion of the locational figure concerned. 

The foregoing analysis has brought the attracting power of' 
labor location (its ability to substitute "labor orientation" for 
"transport orientation") into the realm of precisely determin- 
able laws, the conditions of which have for the individual case 
been sufficiently clarified by the foregoing. 




It remains to introduce into the framework of our general 
discussion the conditions under which, in the individual instance, 
deviation and labor orientation can and will occur, and thus to 
pass on to the general conditions on which labor orientation de- 
pends. In this connection we shall ask at once two questions: 
First, which of these conditions presents characteristics of in- 
dividual industries; and second, which are conditions applying 
uniformly to all industries — in other words are "environmental 
conditions"? We shall see that, in contrast to the basic trans- 
port orientation of industry, which through the material index 
and the '^locational weight" depends solely upon "character- 
istics" of the individual industries, the amount and kind of 
labor orientation is essentially determined by "environmental 

Let us first deduce the various possible kinds of conditions 
from the individual analysis we have undertaken. The fol- 
lowing are the factors on which the deviation of an industrial 
production because of labor locations depends: First, the geo- 
graphical position of the location figures and labor locations. 
Second, the course of the isodapanes around the minimum points 
of the locational figures. Third, the indices of economy of the 104 
labor locations per unit weight of product. 

The geographical position of locational figures and labor lo- 
cations evidently has nothing to do directly with the general char- 
acter of the various industries. It is a seemingly "accidental" 
fact in the situation, independent of the character of an industry. 
We shall, however, later put this fact into its general context 
and take it out of the sphere of the individual and accidental in 
which it seems to stand. 

The course of the isodapanes around the minimum points of 
the locational figures depends upon two subordinate factors. 
One is entirely imphcit in the nature of the given industry, 
namely, its material index and the locational weight dependent 



on it. The figures of the Appendix show (what we shall presently 
discuss more in detail) how completely the distance, and to 
what degree the form of the isodapane is dominated by this 
factor. For the distance of the isodapanes from each other, how- 
ever, a second factor becomes operative, namely, the rates of 
transportation prevailing at any given time in a region. It is 
clear that if one draws around a point lines indicating equal 
additional transportation costs, i.e., lines whose distance from 
each other is determined by a given unit of additional cost, the 
actual geographical distance of these lines from each other will 
be determined among other things by whatever geographical dis- 
tance the unit rate of costs covers, i.e., by the height of the pre- 
vailing rates of transportation. Here we have a further condition 
of labor orientation independent of the character of individual 
industries and applying equally to all of them. 

3. In order to see upon what the indices of economy of the 
labor locations per unit weight of product depend, we shall have 
to inquire how such an economy (for example, of ten marks per 
ton of product) works out. Evidently, because the labor costs 
per ton are "compressed" by a given percentage, 5, 10, 20 per 
cent, etc., the index of economy depends first upon this per- 
centage of ''compression." But that is only one factor. How 
great the total absolute economy per ton will be depends also, it 
is obvious, upon the absolute level of labor costs which are com- 
105 pressed. If these costs amount to M. 1,000 per ton, a compres- 
sion of 10 per cent will cause an index of economy for this 
labor location of M.ioo per ton; but if they amount to only 
M.io, the index will be M.i. This absolute amount of labor 
costs per ton of product on which the compression is based (and 
which is in a certain sense the object of this compression) evi- 
dently pertains to every given industry of a country in a given 
stage of development in the form of average costs of labor which 
must be applied to the ton of product. We shall call this the in- 
dex of labor cost of the industry. As a condition of labor orienta- 



tion the labor costs accruing per ton of product therefore belong 
to the characteristics of the particular industries. 

The percentage, however, by which a given labor location 
compresses this index of the cost of labor of an industry is not a 
peculiarity of the given industry but one of the particular labor 
location.^ Therefore the actual percentage of compression of the 
labor cost indices at the various labor locations constitutes a 
third general environmental condition. 

There are thus two general characteristics of industries de- 
termining their labor orientation: (i) their locational weight 
(especially their index of materials), and (2) the index of their 
labor costs. And there are three environmental conditions deter- 
mining labor orientation : ( i ) the geographical position of loca- 
tional figures and labor locations, (2 ) the rates of transportation, 
(3) the actual percentages of compression of the labor cost 


Let us take up first the characteristics which we have said 
to be factors in determining the labor locations of individual in- 
dustries, that is, let us examine the manner in which the loca- 
tional weight, or index of materials, and the index of labor costs 
determine labor orientation. 106 


I. Index of labor costs. — The significance of the index of 
labor costs is very simple and really already evident. The for- 
mula, according to the foregoing, will run: With a high index of 
labor costs, a large quantity of labor costs will be available for 
compression, with correspondingly large potential indices of 
economy of the labor locations, and correspondingly high crit- 
ical isodapanes; therefore we shall find a high potential attract- 
ing power of the labor locations. And vice versa: low index 
of labor costs, small quantity of labor cost available for com- 

^ This is certainly true for the labor locations of the same industry. 


pression, etc. That is to say, the potential attracting power of 
the labor locations runs, for the different individual industries, 
parallel to the indices of labor costs of the industries. The index 
of labor costs is the provisional standard of measuring the extent 
to which the industries may be deviated. For many industries it 
alone decides definitely how they will be oriented ; this is true for 
all those in which the labor costs are so low that they are insuf- 
ficient to cause effective indices of economy. The other indus- 
tries are grouped by this index according to the amount of labor 
they require per ton of product, which primarily indicates to 
what extent they may be deviated. 

2 . The locational weight. — In order, however, to obtain the 
actual standard for measuring to what extent an industry may 
be deviated, we must take into consideration the locational 
weight and the index of materials. ) 

The locational weight influences the extent to which an in- 
dustry may be deviated through its effect upon the distance and 
form of the isodapanes. Speaking first of the distance of thel 
isodapanes, the manner in which the locational weight affects 
them is theoretically very simple: low locational weight, small! 
mass of material per ton of product to be transported, great dis 
tance of the isodapanes from each other, wide extension of the 
critical isodapane; consequently the industry may be deviat 
to a large extent. And vice versa. The locational weight repr 
sents a standard which further determines the distance of th 
isodapanes for the particular industry. To the extent that it af 
fects this distance, it simply provides a more precise determina 
tion of the provisional standard furnished by the index of laboi! 
107 costs in the foregoing formula. 

However, the locational weight affects not only the distance 
between the isodapanes from each other but also their formsi 
It does so through the size and composition of the material inde?l 
on which it rests, as the figures of the Appendix show. It can also 
tell us that the tendency of a given industry to deviate from tht< 


minimum point is not necessarily of equal force in all different 
directions. So far as we can set up a general rule, only industries 
which have components of equal strength determining their lo- 
cation (and hence having a centrally situated location) have a 
tolerably equal tendency to deviate their location from the mini- 
mum point in all directions (approximately circular form of 
the isodapanes). An industry having components of varying 
strength, and hence an eccentric minimum point (i.e., with a 
minimum point near one corner or in it), will more easily deviate 
in the direction of the strongest corners of the location, and the 
stronger its components are, the more it will do so. Expressed 
in terms of the use of materials, the industries having a very 
small material index (very little localized material and hence 
preponderance of the consumption-components) and industries 
having a very high material index (a great deal of localized ma- 
terial and hence preponderance of some material component) 
will deviate unevenly (deviation in the direction of the enlarged 
corners being easier). Industries, on the other hand, with a 
medium index of materials (for instance of the size of 2), par- 
ticularly if it is also evenly composed (1:1), will deviate more 
Dr less evenly in all directions. 

All this, however, is not of very great importance. It is of 

significance only for deviations over short distances, really only 

■or deviations which lie within or in the immediate vicinity of 

he locational figures. For all greater distances the isodapanes 

ipproximate (as the figures of the Appendix show) the form of 

■I circle, whatever the size and composition of the material index. 

\nd this is quite to be expected, for the situation of the location 

esulting from the material index becomes a matter of indiffer- 

nce for great distances, for which the locational figure approxi- 

lates more and more a "point." The deviation represents more 

nd more transportation back and forth on the same line, and 

pll therefore be equally expensive in all directions. The ma- 108 

^rial index of an industry, through the form which it gives to 


the isodapanes, besides its effect upon the distance, becomes 
geographically significant for small deviations by altering the 
^'direction" in which such deviation would turn under the in- 
fluence of the index of labor costs; by thus altering the "direc- 
tion" of possible deviations, the material index affects the shape 
of the isodapanes, besides determining their distance from each 
other. But this influence disappears for greater distances. And 
since the geographical difference of direction is, as the figures 
show, none too great even for the short distances (for the isoda- 
panes even then approximate rather closely the form of circles), 
it is permissible for the broad purposes of our theory to ignore 
the material index in so far as its significance is based only upon« 
the non-circular form of the isodapanes. The theory should be^ 
allowed to proceed as if all isodapanes were circular; in which 
case only the distance resulting from the absolute quantity of 
material used remains for determining more precisely the real 
deviating significance of the index of labor costs of the labor 
locations through the locational weight. 

3. Locational weight and coefficient of labor. — To deter- 
mine more precisely through the locational weight the real devi- 
ating significance of the index of labor costs measured (it will 
be remembered) by the number of tons of product, we have to 
bear in mind that every increase of the locational weight dimin- 
ishes (by contracting the isodapanes) this real significance, whil 
every decrease of the locational weight increases the significance 
The real deviating significance cannot be measured by weigh 
of product (as has been done by the index of labor costs so far) 
but only by locational weight (weight of product plus weight oi|| 
localized materials). Expressed differently, the amount of laboK 
costs connected with the locational weight of a given industry 
in the coefficient of labor, as we shall call it, constitutes the gen 
eral characteristic determining labor deviation of the industry. |j 

Indeed, it is quite clear that if the form of the isodapanes 
(i.e., the different degree of deviation in different directions) 


may be disregarded, it is the locational weight that has to be 
moved if a deviation is to take place. This locational weight, 
therefore, is the only factor which balances the actual deviating 
influence of the labor costs as they are being compressed. But if 109 
the varying degree of deviation of industry in various directions, 
and if the qualitative determination of its deviations by the loca- 
tional weight and its composition are matters of indifference, 
then the locational weight may be contrasted with the amount of 
labor costs simply as a quantitative measure of the extent of its 
deviating ability, and thus be made the basis of calculating this 

The concept of the "labor coefficient" does this. It might be 
well to point out in this connection that these labor coefficients 
will be fractions, like 100/3 (i-^-? M.ioo labor cost per ton of 
product to three tons locational weight). It will be useful, how- 
ever, to get the labor coefficient of different industries on a 
fully comparable basis. We shall therefore reduce it so that the 
locational weight becomes one. In other words, we shall ask 
how much labor cost will arise in each industry for one ton of 
locational weight to be moved. We shall always speak of the 
labor coefficient of an industry in the sense of its labor costs per 
ton of weight to be moved, per locational ton, as we may call it.^ 

Using the term labor coefficient in this sense, we shall hence- 
forth say that the labor orientation of industries, so far as it de- 
pends on their general characteristics, is determined by their 
labor coefficient. 

To illustrate the significance of this theorem we shall give a 
few examples. The manufacture of corsets has a labor coefficient 
3f about M.I, 5 00; the pottery industry, of about M.55; the 
Droduction of raw sugar (from beets), of M.1.30. According to 
:hese coefficients, 10 per cent of labor cost saved at any place 
iiieans respectively M.150, M.5.50, and M.0.13 saved per loca- 

* Every such locational ton must be thought of as composed of amounts of 
product and materials corresponding to the composition of the locational weight. 



tional ton. If we assume a ton-kilometer rate of 5 pfennig, we 
find that the corset manufacture might deviate 3,000 km., the 
no pottery industry, no km., and raw sugar production, 2.6 km. 
The entire — and immensely different — manner of orientation of 
these three industries is explained by these figures. 


We have spoken hitherto of the location of isolated individ- 
ual productive units which are being deviated. It is not difficult 
to visualize the evolution of the orientation of an entire industry 
under the influence of the labor coefficient and of its compressi- 
bility. It is quite easy to get a picture of this orientation. We 
should, first, consider how far the individual productive units of 
a given industry may deviate from the minimum points of the 
individual locational figures, this being determined by the par- 1 
ticular labor coefficient. And we should, second, remember that( 
theoretically each attracting labor location will influence all the 
locational figures of an industry, wherever they may be situated 
and that each attracting labor location has a tendency to attract 
production from all sides to itself. From these two considera- 
tions we get the picture of production piling up at the labor loca- 
tions, coming from various directions. It is important to observe 
that the number of locations where they will pile up is related to 
the extent of the deviation. This last shading of the picture may 
also be seen by combining the two considerations. For if the 
attraction of the labor locations of an industry, affecting as i1 
does the locational figures from all sides, is effective over large 
areas, this will mean an effective competition of the variom 
labor locations with each other. Some labor locations of the 
same industry will compress the labor costs more, and therefore' 
some will exert a stronger attraction than others. Those whidl. 
attract more strongly — which attract with the larger percent!, 
age of compression — will eliminate those which attract lesJl 
strongly. Within the radius in which they are effective (depend i 


ing on the character of the industry) they will draw production 
to themselves from all sides. This power of attracting industries 
from all sides, of eliminating the "weak," will be proportionate 
to the effect of the labor locations of a given industry, and this 
effect depends upon the extent to which an industry will deviate. 
The result will be that industries deviating to a high degree will 
agglomerate in a small number of labor locations, while indus- 
tries with a low degree of deviation will remain distributed over 
many locations. 1 1 1 

As a result of our consideration of the labor coefficient we 
can state the following rule about the orientation of an entire in- 
dustry: Since the deviation of an industry depends on the size of 
its labor coefficient, the industry will be concentrated at a smaller 
number of labor locations, will tend to be more strongly oriented 
according to labor, the higher its labor coefficient is. 

All this is clear, and would have been accepted as true even 

before the idea of orientation as a whole had been set forth in 

detail as we have just done. We could now leave the subject of 

the orientation of an entire industry if there were not still one 

point relating to the "concentration" which should be clarified. 

This point concerns an alteration in the attracting power of the 

labor locations which takes place through (hindurchgeht) an 

alteration in the costs of transportation in the process of con- 

'centration. Let us, for example, imagine the simplest case in 

which the production of two locational figures is concentrated 

at one labor location, as is shown graphically in the Figure 18 

shown on p. 115. The labor location to which the industry is 

attracted would draw each of the raw materials which it needs 

'from a different material deposit (the first materials from Mx 

nd M\, and the second from M2 and M'2, and if the industries 

f more than two locational figures were attracted, it would draw 

from as many material deposits as there were locational figures 

Dresent, assuming that the industry of each of the locational 

igures had its own material deposits. It is clear, however, that 


for each of the materials used there is one deposit which is most 
favorably situated in relation to the labor location. And it is 
quite evident that, assuming a sufficient productivity of this 
most favorably situated deposit, the industry when removed to 
the labor location will no longer need the less favorably situated 
materials which it made use of in the individual figures. It will 
therefore "close down" those deposits and cover its needs from 
112 the one most favorably situated. In our case this will mean that 
Ml and M\ will be closed down, and the whole demand for raw 
materials will be supplied from M2 and M\. A labor location 
which has attracted plants will be connected with all the in- 
dividual locational figures of the industry only through the mar- 
kets for which it produces, and not any more through their ma- 
terial deposits; and it markets its goods "all over the world" (as 
we can daily observe), while it uses only the nearest deposits oj 
sufficient productiveness for its raw material. 

The closing down of raw material deposits which is the char- 
acteristic feature of this phenomenon takes place for the pur 
pose of saving unnecessary costs of transportation. Its result i: 
that in every locational figure whose industry is diverted th«< 
total deviation costs of the old locational figure are no longer s( 
up against the labor economy which the diverting labor locatioi 
offers ; from these deviation costs the amount of transportatioi 
costs saved by using the most favorable deposits is now to 
subtracted. In our case the economy which A offers is no longe^ 
contrasted to the full deviation costs of Mi Mo C or M'l M\ C:\ 
since so far as the deviation of the first triangle is concernec 
these deviation costs are to be lessened by the transportatioi 
costs saved by substituting M'l for Mi ; and so far as the devn 
tion of the second triangle is concerned, by the economy whicli 
the substitution of M2 for M'2 offers. These economies of transj 
portation are evident from the different length of the hues to th' 
deposits. Cf. Fig. 18 on next page. 

Now in order to make this tendency even clearer we ma; 


express the matter the other way around. We may say: to the 
economy which the labor location offers through lower costs of 
labor is added that which it gains through replacement of the 
material deposits. Therefore in order to make clear the actual 
attracting power of a labor location in relation to any given loca- 
tional figure we shall have to set against the deviation costs of 
this locational figure, not simply the index of labor economy of 
ithe location, but also the economies gained through the replace- 
ment of material deposits. Only in this manner shall we gain a 


Mi Ml 

Fig. 19 

measuring rod for the attracting power of the labor location, 
irst, in its effect upon each individual locational figure, and sec- 
ond, in its compound effect upon all locational figures which fall 
vithin its circle of influence. And only thus do we gain a correct 113 
heoretical picture of the orientation of an industry as a whole, 
md of the magnitude and form of its concentration at the labor 

It may even be that new deposits of materials are called into 
)lay by such a deviation. This opening up of new deposits, as 
Veil as the replacement of material deposits, may have essential 
ignificance with respect to the competition of the labor loca- 
: jions with each other, and may codetermine the deviation of 
■ tidustry. It is obvious that new deposits may be brought to light 
^y the deviation. For the utilization of material deposits natu- 
ally need not be limited to those originally connected with the 
Dcational figures, but may obviously include deposits hitherto 


not used, which lie in the vicinity of the labor location. Figure 
19 shows a very simple case. The larger or smaller chances of 
making use of favorably situated new deposits (as in general 
the possibility of replacing those situated far away from the 
labor location by similar deposits nearer at hand) is of course 
a factor in selecting the labor locations. Locations which have 
material deposits in their neighborhood and have an opportunity 
to bring about effective replacements in case of deviation will 
eliminate such others as do not have such opportunity precisely 
to the extent to which the attracting power of their index 0^ 
economy is increased by economies of transportation costs. ^ A\ 
we have seen from the preceding discussion, only the possibility 
of replacing material deposits limits the real amount of devia 
tion. It is clear that such replacements influence the choice of thi 
114 labor locations, and thereby the concrete picture of deviation. 
The general extent of the deviation of the industry depen 
upon its labor coefficient. The higher this coefficient is, and 
greater the distance over which deviation takes place on acco 
of it, the greater will be the distances which the replacemen 
will cover, the more effective will be the economies in transpo 
and the more will these economies strengthen the attract 
power of the labor locations. The attracting power of labor 1 
tions of an industry will not increase precisely parallel to 
labor coefficient, on account of the increasing replacements; f 
will increase more than proportionally. The general rule thajl 
the coefficient of labor determines the divertibility of an industrll 
may be more exactly formulated. Coefficient of labor and divert: 
bility of an industry may be compared to two rising lines, th 

° Of course we can calculate precisely how the attracting power of one l£ 
bor location in comparison with that of another will be affected by this poss 
biUty of replacement. We need only compare the distances of the labor locatioi 
from their nearest material deposits. By precisely the amount that the distan« 
from one labor location is shorter than the distance from another, the econom 
in the case of that labor location will be greater than in the other. A propo:j 
tionate amount is to be added to its index of economy. 


rise of one depending upon that of the other; although the 
rise of the deviation line exceeds that of the labor coefficient 
line. We may explain this fact by saying that the divertibility 
is not a phenomenon simply parallel to the labor coefficient, but 
a more complex functional phenomenon. Industries with really 
I high labor coefficients will therefore at the same time be very 
I strongly agglomerated. 


Two environmental conditions of divertibility seem to be 
quite accidental and to defy statements in terms of a general 
rule: the mutual distance between locational figures and labor 
locations, and the indices of economy of the labor locations.^ 
This appearance is borne out by the facts to a certain extent. For, 
whatever general rules we may formulate, the actual situation of 
a given locational figure in relation to the given labor locations 
will always be different for each instance, and the actual per- 
centage of compression of labor costs will remain a specific one 
for each location. From that, however, it does not follow that 
these conditions do not take place within the limits of a general 
Irule, for in fact they do. Both the mutual distance between loca- 115 
tional figures and labor locations are, in general, dominated by 
ithe same pair of internally interrelated facts, the density of 
Ipopulation and the level of civilization. 

It is clear that in sparsely populated regions having markets 
di consumption widely apart from each other the locational 
figures with their minimum points will be distributed at great in- 
tervals over the country; similarly "labor locations" will be 
fnore thinly scattered over the country than in densely popu- 
lated regions. Therefore the average distance between the loca- 
tional figures and the labor locations will be large. On the other 
land, a dense population will mean that one locational figure 

^ This statement involves : ( i ) the distance between the locational figures, 
2) the distance between the labor locations, (3) the distance between the loca- 
ional figures and the labor locations. — Editor. 


will lie closer to another, one labor location beside another labor 
location, and hence that a short average distance between loca- 
tional figures and labor locations will prevail. The ranges of 
deviation to be overcome will thus vary according to the density 
of population. An increasing density of population will always 
mean that shorter distances have to be overcome, and that there- 
fore more and more favorable conditions for deviation will re- 
sult. That is the general rule to which this seemingly accidental 
and unrelated point is subject. 

With a rather extensive claim to general validity we may 
further say that thinly populated regions will be culturally back- 
ward, or better, culturally "undifferentiated." The efficiency of 
labor will not be very different for different locations; and like- 
wise the wages will not vary greatly. The differences of labor 
costs will hence be small and their relative percentages of com- 
pression low. Vice versa, the differentiation of labor costs and 
the relative percentages of compression of the labor costs will 
increase with an increasing density of population. That is the 
general rule to which this condition is subjected. 

Both together (the distances between locational figures and 
labor locations, and the indices of economy of labor locations) 
will be influenced by the density of population and the accom- 
panying rise of civilization in such a way as to facilitate increas- 
ing labor orientation, since increased percentages of compres- 
sion, like lessened ranges of deviation, of course facilitate the 
ii6 removal of production to the labor location. It may therefore 
very well be that in sparsely populated regions industries are 
predominantly oriented according to transportation facilities,! 
whereas in more thickly populated regions they are predomi-i 
nantly oriented according to labor. 

Finally, the significance of the third environmental condi-' 
tion, of the transportation rates, is very simple. Whenever the 
rates per ton-kilometer decrease, the isodapanes indicating devi- 
ation costs go farther apart and the indices of economy of labor 


locations are lowered proportionately. As a result, labor loca- 
tions much farther away will effectively attract; or in other 
words, orientation according to labor will influence a larger and 
larger part of the whole body of industry, measured quantitative- 
ly by units of production. It will concentrate the production of 
diverted industries more and more at the most advantageous 
labor locations by extending the sphere of attraction of these 
locations. That is the general rule to which this environmental 
condition is subjected. 

We may look upon a good part of the struggle between 
handicraft and large-scale industry in the second half of the 
nineteenth century as a proof of this rule concerning the results 
; of decreasing transportation costs. It has already been indicated 
! how far the decline of the handicrafts means the disappearance 
of production from the markets of consumption, due to changes 
j in the material index of the industries. Now we may say that 
: this decline was hastened by the fact that the railways facilitated 
the deviation of industry toward the most favorable labor loca- 
tions. Local differences of the indices of labor costs (which had 
been rather veiled, so to speak, by costs of transportation) be- 
came suddenly apparent and of practical significance when rail- 
way rates began to decline rapidly. Thus good labor locations 
have collected around themselves large masses of industry which 
had formerly been oriented transportationally; that is, had been 
situated near the market and could therefore be organized on a 
handicraft basis. In the second part we shall show to what in- 
dustries this applies particularly.^ But at this time we may ask 
•what has removed products like furniture, baskets, casks, etc., 
away from the places of consumption (where they used to be 
produced by handicraft) toward the best labor locations where 

^ As has been pointed out, this second part has never been written by A. 
Weber; but studies of individual industries by some of his students have been 
published under his direction by J. C. B. Mohr, in Tübingen. See also Introduc- 
tion. — Editor. 


their manufacture takes place for purposes of marketing them 
on a large scale, though often the conditions of manufacture are 
117 technically not greatly changed. We shall find that this change 
has been caused by the lower transportation rates. 


All changes of environmental conditions have the tendency 
to promote labor orientation. For the general course of develop- 
ment is apparently in normal times not only in the direction of 
decreasing transportation costs but also in the direction of facili- 
tating deviation by increasing the density of population and the 
differentiation of culture. 

On the other hand, the same technical developments which 
diminish the costs of transportation change, pari passu, the gen- 
eral character of the industries by mechanizing the process of 
production. This decreases the labor coefficient of the industries, 
altering simultaneously both its factors, the amount of labor 
used and the amount of material used per ton of product. Ob- 
viously, it increases the amount of material used through the use 
of coal and of weight-losing materials; at the same time it ren- 
ders manual labor superfluous and thus diminishes the amount 
of labor used. In consequence there is less and less labor neces- 
sary for a greater and greater locational weight. The result is a 
tendency continually to convert labor-oriented industry into 
transport-oriented industry. If we wish by means of our theory > 
to make fully clear the whole meaning of this tendency toward! 
integration, it can be done by keeping in mind on the one hand 
the convergence of the isodapanes which is a consequence of the 
increase of the index of materials and which represents the ''dif 
ficulty" of deviation, and by realizing on the other hand how the» 
decreasing compressible quantities of labor costs per ton of 
product reduce the economy values of the labor locations, thus 1. 
pushing the critical isodapanes of the labor locations more close- 1. 
ly toward the minimum point, and again diminishing the possi- 


bility of deviation. If we think of both these things together, we 
can see that the integrating tendency which results from the me- 
chanization of the process of production must be very strong. 11 

Whether it will be stronger than the ^'disintegrating tend- 
encies" discussed earlier, which also lie in the historical develop- 
ment, cannot be determined in abstracto. For only two of the 
opposed integrating and disintegrating forces (namely, the de- 
creases of transportation costs and the increase of amount of 
material used) may be set in relation to each other abstractly 
and their net effect evaluated by means of more or less well- 
known facts. For the purpose of a provisional understanding of 
the tendencies of the development as a whole it will be worth 
while to investigate the relationship of these two. 

An increase in the use of raw materials means an increase in 
the amount of weight which, in case of a deviation from the 
minimal point, must be transported. Decrease in the rates of 
transportation means increase in the amount which can be trans- 
ported at the same expense. If the amount of material used by 
an industry should be doubled, but the rates of transportation 
should be at the same time reduced by one-half, the effects would 
balance and everything would remain as before as far as the 
divertibility of the industry is concerned. The position of the 
isodapanes would remain the same. The tendency to push them 
apart (decreases in transport rates) and the tendency to draw 
them together (increases in the material index) balance each 
other. Starting then from this generalization, we may after all 
say something about the total effect of the integrating and dis- 
integrating tendencies during the second half of the nineteenth 
century. The gigantic cheapening of transportation caused by 
steam has reduced the rates per ton-kilometer to one-fourth, 
one-tenth, even one-twentieth of what they were formerly. Now 
there are probably not many industries in which the mechaniza- 
tion of the process of production (however greatly it may have 
expanded with the aid of steam) has increased the weights to be 


transported to quite that extent. That, however, would have 
been necessary in order to balance completely the general tend- 
ency of the isodapanes to expand when transport rates decrease. 
Hence on the whole they must have been widened, for some in- 
dustries more, for others less, according to the extent of their 
mechanization, but on the whole in all industries to a significant 
119 extent. 

From the unchecked widening of the isodapanes to four and 
ten times their extent (as was bound to happen in all sections of 
industry not yet affected by mechanization) we get a picture of 
the revolution in the locational conditions for these even now 
rather large sections of industry — a revolution due to the enor- 
mously extended spheres of attraction of the labor locations in 
them; and we get a picture of the extent to which, for instance, 
the struggle between handicraft and manufacturing industry 
may be conceived simply as a consequence of this increased 
power of attraction. 

That the widening of the isodapanes is impeded in those 
industries which are being mechanized leads us to the follow- 
ing considerations: In so far as such widening occurred — and 
as we have seen, that was predominantly the case — a loosening 
of industries and a strengthening of the labor orientation must 
have taken place. Since, now, a decrease in the indices of econ- 
omy of the labor locations means a pushing of the critical isoda- 
panes toward the minimum points, we get the following picture 
applicable to the development of the mechanized parts of indus- 
try: the isodapanes are pushed apart (widened) and at the 
same time the critical isodapanes are pushed back farther to- 
ward the inside of the concentric rings formed by the widening 
isodapanes. Only in the cases in which, as a result of both these 
movements, the pushed-back critical isodapane was farther 
from the minimal point than it was prior to the mechanization 
and decrease in transportation costs has there been any loosen- 
ing up. It is part of the empirical study to show whether that 


was in fact the case for large portions of industry, and whether 
transport or labor orientation has on the whole progressed far- 
thest, and furthermore, which of the two is still progressing today. 
With this final application of these questions to concrete 
reahty it is now possible to take leave of the laws of labor orien- 
tation so far as pure theory is concerned. To determine, on the 
basis of the rules we have discovered, to what extent industry is 
labor-oriented and to what extent transport-oriented will be seen 
to be one of the principal tasks of the study of the empirical mate- 
rial. It will be evident that this empirical study is one of the 
best means of checking up the correctness of our theory by an 
appeal to the facts. For the general criterion here set up of the 120 
abihty of industry to orient itself toward labor, its labor coeffi- 
cient, is a clear characteristic of industries, not very difficult 
to ascertain in reality. It ought to be possible to verify the signif- 
icance of the labor coefficient of any industry for the deviation 
of its industrial location from the minimum points. 121 



Costs of transportation and costs of labor are the only two 
factors in location which work regionally. All others work, as we 
have seen, only as part of the agglomerative or deglomerative 
forces contributing to local accumulation or distribution of in- 
dustry; and so they operate only within the general frameworks 
formed by the regional factors. Our present task is to introduces 
the effect of these factors into the general theory. 



The first thing which must be done at this point is to show- 
that in principle the theory does not need to interpret agglomera 
tive and deglomerative factors as two groups, but as one group ij 
namely, as agglomeration. All deglomerative factors are by theii 
very nature nothing but counter-tendencies resulting from ag 
glomeration. But if that is what they are, theory may disregard j 
them as independent factors and treat them as the opposite o 
agglomeration. For the theory is not concerned with the dy- 
namic interaction of operative tendencies toward agglomeratio: 
and resultant contrary tendencies toward deglomeration, bui 
rather with the final effect of this process, since only this finaii 
122 effect alters the locational situation. 

However, this final effect may be that the agglomerativ 
tendencies are completely paralyzed (in which case there is nc 
alteration of the locational picture we have already gained), d 
it may mean that there is a permanent excess of the tendency t( 
agglomeration (in which case theory has to introduce this factor 



of agglomeration as one which may possibly change our previ- 
ous picture). Theory has, therefore, as a matter of fact to deal 
only with possible agglomerations — agglomerations which are 
a resultant of complicated processes. 

Nevertheless it would be desirable if the abstract theory 
were able to analyze into its component parts the dynamic inter- 
action of agglomerative and deglomerative factors which create 
this ''resultant," if it were able to dissect each group and (as in 
the cases of costs of transportation and costs of labor) determine 
to what degree each individual industry is under the influence of 
each factor. 

Unfortunately this cannot be done by pure deduction. Both 
of the hitherto considered causes of location were simple quanti- 
ties which could be deduced from the known facts of some iso- 
lated industrial process, and their degree of influence upon each 
industry could also be deduced from these facts. The groups of 
locational factors now to be considered are, on the contrary, dis- 
tinguished by the fact that they result from the social nature of 
production, and are accordingly not to be discovered by analyz- 
ing an isolated process of production. x\nd in the case of these 
social factors of concentration it is absolutely impossible to say 
2 priori whether production costs would be lower or higher. 
There is no complex of known premises from which such a propo- 
rtion could be deduced. We have only empirical knowledge of 
individual facts to tell us that certain elements of industry be- 
:ome cheapened in the process, others more expensive. Since we 
:annot know within the compass of general theory the groups of 
special locational factors composing the agglomerative and de- 
!?lomerative tendencies, it is of course impossible to discover by 
leduction definite general diaracteristics according to which we 
could determine the extent of the influence of these agglomera- 
tive and deglomerative factors upon the individual industries. 123 

Thus the task of general theory is here of necessity much 
nore limited than in the preceding sections. Speaking precisely. 


theory can have only the task of finding quite general rules con- 
cerning the manner and extent of the effect of the agglomerative 
tendencies upon location; it must rely upon empiricism to dis- 
cover individual agglomerative and deglomerative factors and to 
apply the general rules of agglomeration to the various indus- 

It is, however, worth while to give a certain foundation in 
fact (without claiming completeness) for our discussion. Ac- 
cordingly there follows a short survey of the more essential fac- 
tors known to work in an agglomerative or deglomerative man- 
ner. As the discussion proceeds, it will become clear that it is 
possible to make at least a beginning of a preliminary grouping 
of industries, and this as a matter of pure theory. 


An agglomerative factor, for purposes of our discussion, 
an ''advantage" or a cheapening of production or marketin| 
which results from the fact that production is carried on to some 
considerable extent at one place, while a deglomerative factor 
a cheapening of production which results from the decent raliza-' 
tion of production (production in more than one place). In the 
case of each concentrated industry the interaction of agglomera- 
tive and deglomerative factors must always result in certain in- 
dices of costs per unit of product, indices which are a function of 
the amount of concentration. If these indices of costs are smaller 
in case of great concentration than they are in cases of little con- 
centration, they clearly become for the industry in question in- 
dices of economy. They point out that with a certain degree of 
concentration the costs are smaller on account of concentration. 
They are smaller by a certain amount per unit of product than 
they would be in the case of complete dispersion of the industry, 
or than they would be in a case involving less concentration. 

We shall deal with these indices of economy by making use 
of the expression the function of economy of agglomeration, 



or more briefly the junction of economy of an industry. The 124 
expression function of agglomeration might be used if it were 
not better to reserve this latter term for another relation which 
will become important when we try to establish a precise arith- 
metical determination of the quantities of agglomeration (cf. 
Appendix III, §2). 

The function of economy is composed of individual indices 
of economy (per unit of product) which correspond to each stage 
of concentration. If there are several such stages of concentra- 
tion, each of which results in an additional saving in costs per 
unit of product, the industry has a true function of economy. If, 
on the other hand, the saving results from a particular definite 
:amount of concentration, and does not continue to increase in 
■case of further concentration, then that industry has merely a 
fixed index of economy of agglomeration. It is obvious that for 
a complete understanding of both these concepts the effect of 
the deglomerative factors must be taken into account. For the 
present, in order to explain the origin of either this function of 
jeconomy or this fixed index of economy, we shall need to analyze 
the various agglomerative and deglomerative factors. 


A. Agglomerative factors, i . We may in the first place, as re- 
gards the agglomerative factors, distinguish between two stages 
bf agglomeration at which these factors are operative. The first 
md lower stage is that of the concentration of industry through 
he simple enlargement of plant. Every large plant with a round- 
ed out organization represents necessarily a local concentration 
Ls compared with production scattered in small workshops over 
ihe neighborhood. The well-known economic advantages of 
arge-scale production as compared with small-scale production 
n.b., not the advantages of the large enterprise as compared 
dth the small enterprise ; we have nothing to do with that) are 
ffective local factors of agglomeration. A certain minimum of 


agglomeration makes the application of a given technical appli- 
ance in the plant possible with a certain percentage of saving; a 
further minimum of agglomeration makes possible a particular 
form of labor organization in the plant, — this also with a certain 
125 percentage of economy; and finally a certain minimum of ag- 
glomeration enables a plant to enter into the economic relation- 
ship which makes possible cheap large-scale purchasing, cheap 11 
credit, etc. These agglomerative factors combined create the 
large-scale plant of minimum efficient size for the industry in 
question. The coefficient of economy of the large plant as com- 
pared with the small (index of large-scale production) is also the 
coefficient of agglomeration of each industry, as far as this stage 

2. Whether an industry will agglomerate because of only 
this tendency to concentration through extension of plant, or 
whether it will come under the influence of a further tendency 
to concentration, depends upon the extent of the advantages re- 
sulting from close local association of several plants. In order to 
get a preliminary systematic survey ("preliminary" I again em- 
phasize) of this social agglomeration, let it be noted that thej 
local aggregation of several plants simply carries farther the ad- 
vantages of the large plant, and hence that the factors of agglom- 
eration which create this higher stage of social agglomeratioi 
will be the same as those which created the large-scale plant, 
essential factors of this higher stage of agglomeration we agaii 
list the development of technical equipment, the development oi 
labor organization, and a better adaptation to the economic or^j 
ganization as a whole. 

a) Development of the technical equipment. — ^The complet 
technical equipment which is necessary to carry out a process oif 
production may in highly developed industries become so spe-i 
ciaHzed that minute parts of the process of production utilize || 
specialized machines and that even quite large-scale plants arej 
not able to make full time use of such equipment. Such special-j 



ized machines must then, together with their own parts of the 
, process of production, be taken out of the single large plant and 
i must work for several of them, i.e., become the basis of independ- 
ent auxiliary industries. In theory, the workshops of such aux- 126 
iliary industries may be separated from the main plants for which 
they work, and hence need not lead to local concentration of the 
j main plants. As a matter of fact, however, they form one tech- 
nical whole with the main plants for which they work. And this 
, technical whole naturally functions best if its mutually depend- 
ent parts are locally concentrated, because then all the parts re- 
main "in touch" with one another. The development of such spe- 
cialized machines and of the auxiliary machines belonging to 
them establishes therefore a technical minimum of agglomera- 
tion, and this technical minimum, as soon as it leads to a social 
iconcentration of plants, extends beyond the minimum of plants 
previously considered. It thus becomes a factor of agglomera- 

And a quite similar influence (which yields the same result) 
lis exerted by a second factor which we often find adduced as a 
pause of social agglomeration, namely, the better opportunities 
for replacing and repairing machinery. The workshops for re- 
placement and repair are a part of the technical equipment — in 
1 certain sense its "physician." The highly specialized develop- 
nent of this aspect of production is again possible only in con- 
lection with a large total technical equipment which exceeds the 
;ize of a single plant. In this case also a scattered location of the 
)lants which are to be worked for, "country practice," is pos- 
:.ible ; but the best and cheapest service is to be secured "in town." 
jThe development of these specialized technical functions accord- 
ngly becomes a factor of social agglomeration. 

b) Development of the labor organization. — A fully devel- 
)ped, differentiated, and integrated labor organization is also 
Q a certain sense equipment. This equipment also has parts 
vhich are so specialized that, as a rule, they are not adapted to 



the conditions of a single large-scale plant. Hence they also tend 
to form specialized auxiliary or partial industries; and just as in 
the case of the technical factors discussed before, these trades 
based on ''division of labor" lend to social agglomeration. It is 
127 not necessary to repeat the reasons for this. 

c) Marketing factors. — The last group of factors — those 
creating a more effective marketing situation — ^will also be found 
at the stage of social agglomeration. The isolated large-scale 
plant is more effective than the small one because it can buy and 
sell on a large scale, thus eliminating the middlemen. Being a 
safer investment, it can get cheaper credit. Grouped large-scale 
plants gain still further economies, especially in purchasing raw 
materials and in marketing. In purchasing raw materials the 
concentrated industry develops its own market for its materials 
and from this market it takes these materials in the necessary- 
qualities and quantities at the time of demand. The isolated en- 
terprise, on the other hand, is forced to buy its materials in ad- 
vance and store them. This means a loss of interest for the indi- 
vidual enterprise, and hence an increase of money outlay. Ir i 
economic terms it represents a wasteful temporary tying up 0: 
capital which could otherwise be actively utilized. Then too, ii 
marketing the product, social concentration permits economies 
because the concentrated industry produces a sort of large uni 
fied market for its products. It is even possible that the whol« 
marketing organization of the manufacturer can be dispensec 
with. Visits and direct buying at the place of production ma] 
develop, replacing the traveling salesman. This represents, noi 
only an individual, but a general economic or social saving m 
well, since in the process "labor" or social energy is saved. 

d) General overhead costs. — If for the foregoing and othej 
reasons the best adaptation of industry to the general economic 
environment becomes, at the higher stage we are now consider 
ing, a general factor of agglomeration, it should be pointed om 
also that the diminution of "general overhead costs" which plaj 


a part at the lower level of agglomeration (i.e., in the case of the 
large as compared with the small plant) reappear on this stage; 
I gas, water mains, streets, the whole ''general apparatus" will be- 
come cheaper for the individual enterprise at the high level of 
technical development and effective utilization made possible 
through social agglomeration. 128 

To summarize, if for each industry there is an index of the 
size of the plant (be it low or high depending upon the condition 
of technique, organization, etc., attained at any time) which tells 
us what unit costs per ton of product correspond to each stage in 
the size of plant of the industry, and which represents its tend- 
ency toward agglomeration at this lower stage of concentration, 
these same factors will possibly — they certainly frequently do — 
:arry the plant beyond this stage of agglomeration. 

Therefrom a tendency to agglomeration arises which creates 
social concentrations. These, taken together with the tendencies 
it the lower stage, determine the extent of agglomeration at this 
second and higher stage of agglomeration. This may suffice as a 
Dreliminary survey of the active factors of concentration. 

B. Deglomerative factors. As we have noted, every agglom- 
eration may cause opposing tendencies — increased expenses. 
The balance between the active factors and these opposing tend- 
encies gives us the actual power of agglomeration effective in a 
;iven case. 

These opposing tendencies result from the size of the ag- 
glomeration as such; they have, in contrast to the agglomerative 
actors which are related to particular characteristics of each in- 
dustry, such as technique, level of organization, etc., nothing to 
with these characteristics. Their strength and manner of 
/orking depends solely upon the size of the agglomeration. All 
Igglomerations of equal form and size are subject to them in the 
ame manner. These deglomerative factors all follow from the 
'se of land values, which is caused by the increase in the de- 
land for land, which is an accompaniment of all agglomeration. 


This increased demand increases both the significance of the 
marginal utihty of tracts of land and the discounting of this mar- 
ginal utility by speculative manoeuvers. All deglomerative tend- 
encies start from the increase in economic rent (ground rent). 
We can describe them all as various consequences of economic 

This is not the place to discuss through what various means 
all these consequences take place; still less is it the place to dis- 
cuss the kinds and extent of the effects of the various increasec 
expenses of production. We are concerned only with stating th( 
situation theoretically. Developing further what has alread) 
been said, we have only to note that all these consequences rep 
129 resent merely a weakening of agglomerative tendencies. If w< 
assume, for instance, that economic rent makes the area 
land necessary for an industry more expensive,^ that means ai 
increase of the general overhead costs, of whose diminutioi 
through agglomeration we spoke earlier. If we assume that it in 
creases the costs of labor, it means that part or all of the cheap 
ening of labor on account of highly efficient organization will b 
absorbed. In either case the existence and increase of the rent 
land means, not the operation of fundamentally new factors 
orientation, but alv/ays only a decrease in the effect of the ag 
glomerative factors. But the growth of these counteracting el 
fects will always run parallel to the size of agglomeration as Ion 
as the rent of land parallels the size of the agglomeration, whic 
is generally the case. 

From the foregoing there follow the important conclusion« 
first, that we may think of the importance of the deglomerativ 
factors, even in detail, as a weakening of the agglomerative fac 
tors — a weakening which, appearing under certain circum 
stances, runs parallel to the growth of agglomeration. Secondl} 
while the factors of agglomeration always have application t 

^ Let us assume also that this increase in cost could not be entirely avoide 
by moving the industry to the periphery of an agglomeration. 


separate and individual units of industry or to one or more con- 
nected branches of industry, the weakening of the tendencies to 
agglomeration (created by the agglomerative factors them- 
selves) is connected with only the size — size as such — of the ag- 
glomeration. This weakening therefore comes into existence 
even if the agglomeration is an accidental conglomeration of dif- 
jerent branches of industry, and it follows, since the index of 
economy resulting from agglomeration is always in part deter- 
mined by the extent of the deglomerative tendencies which are 
it the same time called into being, that there can exist theoret- 
'cally ''pure" indices of economy in the case of a single agglomer- 
ated industry, provided it is agglomerated in isolation. But if 130 
)ther industries are added, the resultant weakening of the ag- 
glomerative factors and therefore the size of the indices of econ- 
omy will in part be determined by the fortuitous circumstance 
hat other industries are also agglomerating at the same location. 
Thus the theoretically pure picture of the orientation of an in- 
iustry will be distorted by the actual situation due to agglomera- 
ion. This alteration of reality we shall, following the guiding 
)rinciple of our investigation, for the present leave out of ac- 
:ount. We shall deal here with the tendency to agglomeration and 
ts indices of economy as pure; more strictly speaking, we shall 
)roceed as if the various industries did not disturb each other as 
he result of the coincidence of their agglomeration at the same 

From all this it should be clear — and, through our references 
reality, abundantly clear — in what sense we shall speak of the 
Jidices of economy due to agglomeration and of the "function of 
conomy" as being a composite of these indices (see p. 123). It 
hould further be evident why we, in abstract theory, think of 
jiis "function of economy" as one whose single indices indicate 
iirther and further economies per unit of product as agglomera- 
on increases; and yet these economies grow more and more 
owly as agglomeration increases. For on the one hand we have 


the known facts of experience in the matter, showing that the 
various agglomerative factors, such as the development of tech- 
nique, of organization, etc., in themselves all decrease progres- 
sively. On the other hand this decrease is necessarily accentu- 
ated by the weakening to which these agglomerative factors are 
subjected as the rent of land increases with the size of the ag- 
glomeration. Thus we may think of the function of economy as 
one side of a parabola which approaches more and more slowly 
131 a maximum value. 

It is hardly necessary, I suppose, to explain more fully that 
the ''fixed index of economy," which knows only one stage of ag- 
glomeration and which was on page 123 introduced into the the- J 
ory, is only a theoretical aid, an intermediate assumption to 
which no actual situation ever quite corresponds. For it is evi- 
dent that the factors of agglomeration with which we have be- 
come acquainted will always create a series of stages (with 
attendant growing economies) which range from the stage of ab- 
solute dispersion of location to the theoretical maximum of ag- 
glomeration; and that neither ''absolute dispersion" nor "fixed 
agglomeration of a given size" will ever exist in reality. The as- 
sumption of the existence of this fixed agglomeration will, how- 
ever, perform rather important auxiliary services to our theory. 



The theory of agglomeration deals, according to the preced-| 
ing discussion, with local concentrations of industry which arisi 
because of the fact that the production of a unit of product cai 
in this concentrated producing complex be more economical! 
performed by a certain definite amount. Hence the theory d 
not deal with those local concentrations of production which a] 
pear as the results of other causes of orientation and hence exisi 
quite independently of whether the agglomeration as such has 
any or no advantages. If, as is very often the case, transportation 


facilities concentrate industries near the supplies of raw mate- 
rials, or at the coal fields, or near the big markets of consump- 
tion,^ that phenomenon does not lie within the field of the theory 
of agglomeration. The same is the case when the attracting "la- 
bor locations" develop in such a way as to form large centers of 
agglomeration.^ All these are from our present point of view for- 
' tuitous circumstances in which agglomeration does not form a 
specific element. Our theory of agglomeration has to do only 
with agglomeration as a necessary consequence of agglomerative 
factors as such, not as a fortuitous consequence of other causes 
of orientation; only such part of these other concentrations as 
may be due to independent agglomerative tendencies interests 
us. Hence that agglomeration with which the theory will deal 132 
will be called "pure" or "technical," thus contrasting it with ag- 
glomeration which is incidental to other forces. 


The tendency to agglomeration for technical reasons may 
i first be considered in its effect upon production which is oriented 

solely with regard to transportation and not diverted to "labor 
! locations." What effect would a tendency to agglomeration with 

a fixed index have in this case? 


Assuming for the present that the agglomeration is a case of 
,only one unit with a perfectly definite economy, let us put two 
questions : When will agglomeration take place, and to what ex- 
'tent? And, if it does take place, where will it take place? 

a) When does agglomeration take place, and how much? — 
By means of the concepts of minimum points and isodapanes as 
they have been used earlier it is very easy to develop the answer 
to this question. It is only necessary to recall what was said 
about the indices of economy of the labor locations and their ef- 

See above, p. 71. ^ Cf. above, p. 112. 



feet. The centers of agglomeration also form, with regard to 
scattered production, centers of attraction having particular in- 
dices of economy. If production moves to these centers, that fact 
signifies a deviation accompanied by transportation costs higher 
than those of production located at the points of minimum trans- 
portation cost. And naturally this deviation depends fundamen- 
tally on the same conditions as those set forth on pp. 112 ff. The 
deviation costs per ton of product must be smaller than the econ- 
omies per ton of product. These economies per ton of product 
are indicated by the index of economy of the unit of agglomera- 
tion. The isodapanes indicate the deviation costs per ton of 
product. For every individual part or unit of the production 
complex there must be a critical isodapane the deviation cost in- 
dex of which corresponds exactly to the index of economy of the 
unit of agglomeration. 

If that is clearly understood we can at once see that individ- 
ual units of production become agglomerated and give rise to 
centers of agglomeration if their critical isodapanes intersect, and 
if the quantity of production of each individual unit added to 
that of the other units which participate in the same overlapping 
segment reaches the effective unit of agglomeration. For if such 
critical isodapanes intersect, then for the various individual units 
some common points exist at which the economy of agglomera- 
133 tion is not absorbed by the deviation costs. And when the quan- 
tity of production which can be concentrated at that point reach- 
es the assumed unit of agglomeration, then the agglomeration 
pays ; it can be effectively realized. To state it precisely, the for- 
mation of centers of agglomeration and the agglomeration of in-i 
dividual units of production at these centers depends upon two! 
circumstances: first, upon the existence of intersections of crit- 
ical isodapanes in relation to the assumed unit of agglomeration, 
and second, upon the attainment of the requisite quantity of 
production within these segments. When these two conditions 
are fulfilled, the individual units of production become agglom- 



erated and the concentration affects all parts of the production 
complex. Whatever the situation and whatever the quantity of 
output of any indivdiual unit, if its critical isodapanes intersect 
with those of enough other individual units to make up a unit of 
agglomeration, it will be concentrated with these others. 

For a clarification of the two "conditions" it is necessary to 
note the following, which again is in part analogous to the case of 
orientation as affected by labor. Theoretically, only those pro- 
ductive units can be brought together in the case of each of which 
the economies relating to its particular quantity of production 
exceed the deviation costs, since only for such units does the 
overlapping segment exist. In fact, however, the agglomeration 
can (for the purpose of attaining the requisite amount of pro- 
duction) somewhat exceed this theoretical Hmit and can also at- 
tract certain productive units which are somewhat farther away 
and whose critical isodapanes do not quite reach the segment. 
This may happen if the ratio of economies to deviation costs for 
other parts of the agglomeration is so favorable that a balance on 
the side of economy still remains for the agglomerated industry 
as a whole, even though a part of the economies arising from 
agglomeration must be applied to covering the negative balance 
between economies and deviation costs of such '^fragments"; for 
in such a case the attraction of the ''fragments" will cause lower 
costs for the group as a whole. Beyond such occasional supple- 
menting of units of agglomeration which are not quite complete, 
agglomeration cannot and will not go; because, as will be shown 134 
later, the "effective unit of agglomeration" roughly forms the 
upper limit of agglomeration. Only by throwing together many 
units of agglomeration could a "surplus" be created sufficient to 
attract on a large scale productive units whose isodapanes do not 
reach the segment. Thus this whole matter of agglomeration of 
units which lie too far away when considered by themselves 
means no great alteration — only a comparatively insignificant 
modification — of the two conditions upon which agglomeration 



depends; the basic proposition still holds that a unit of agglom- 
eration with a given index will bring together all those parts of a 
total industry whose critical isodapanes as worked out in terms 
of this unit intersect with each other, if the combined or concen- 
trated production of these parts is sufficient to make up the ef- 
fective unit of agglomeration. 

b) Where will agglomeration take place? — And where will 
the center of agglomeration lie? That also is easily made clear 
by means of the isodapanes. The center of agglomeration must 
obviously lie within the common segments of the critical isoda- 
panes, for within these common segments He the points at which 
production may be concentrated without prohibitive deviation 
costs. Every point within a common segment is a possible point 
of agglomeration; for at any such point production under ag- 
glomerated conditions can take place more cheaply than at the 
scattered points of minimum transportation costs. But where 
will the center of agglomeration actually be located? It will be 
located at that one of the several possible points of agglomera- 
tion which has the lowest transportation costs in relation to the 
total agglomerated output. (See Fig. 20.) 

The various units going into the agglomeration have outputs 
or production of varying size, and the diversion of a large quan- ( 
tity of output toward a point of agglomeration involves greater 
transportation costs than does the diversion of a small quantity 
135 of output. Within the common segments the agglomeration will 
become so situated that the larger units of production have 
changed their positions less than have the smaller ones, for this 
will keep down the total deviation costs. Stated in other words, 
the large units of production will attract the smaller units to loca- 
tions near the former's original minimum points, and will there 
fix the center of agglomeration. 

We can state the result of this dynamic process with great 
precision in the following manner : All the agglomerated produc- ■ 
tive units, together with their common location of production ' 


(the center of agglomeration), constitute one great locational 
figure of the type which is already familiar to us. Its corners are 
the various raw-material supplies and markets of the various 
constituent units. The position of the location in this figure will 
be determined by the components of the different corners pre- 
cisely in accordance with the laws of those locational figures 
which have already been studied. The precise location of the 
center of agglomeration will thus be that of the minimum point 
of transportation cost for this locational figure. It must lie with- 

FiG. 20 Fig. 21 

in the segment of the isodapanes, and within this segment it may 
be quite definitely located. 

c) The size of the unit of agglomeration. — Hard upon the 
heels of the solution of the question as to the point at which the 
production in a given segment takes place there follows the prob- 
lem as to which of several possible agglomerations a unit of pro- 
duction will choose; and this leads to the important rule already 
indicated concerning the size of centers of agglomeration. If the 
isodapanes of an individual unit of production intersect in sev- 
eral areas and in several directions with those of other individual 
units — that is, if an individual unit has several possibilities of 
agglomeration, it will agglomerate within that common segment 
in which the center of agglomeration is least distant from the 
former minimum point of the individual unit concerned. For 


thus the smallest additional transportation costs and the largest 
136 surplus from the index of economy will result. In this connection 
it should be noted that the point of agglomeration is more likely 
to be fairly near to the particular unit concerned when the other 
individual units are situated close at hand, so that the segments 
formed by the intersections of the critical isodapanes are large. 
For illustration compare Figure 21. The actual location, how- 
ever, within the segments still depends upon the relative size 
of the quantities of production concerned, as was shown in our 
previous discussion. In consequence, even though each indi- 
vidual unit tends to choose the largest possible segment (i.e., 
agglomerates with the other units nearest to it), it will also tend 
to choose the particular segment within which the point of ag- 
glomeration is nearest to it. Among the segments in its vicinitj 
it will choose the one in the case of which the smallest possible 
additional quantity of production still suffices for the unit of ag- 
glomeration which has to be gotten together. Put in a slightl> 
different way, and using terribly cumbersome abstract terminol- 
ogy (which unfortunately is nevertheless hardly adequate to ex 
press these matters), we might say: the isolated units of produc 
tion will not agglomerate arbitrarily or indifferently with any 0: 
the others near them; but rather they will agglomerate witl' 
those smallest units which just suffice to make up a requisite unr 
of agglomeration, and which they can attract farthest to them- 
selves, attracting first the smaller ones and then going upward irl 
the scale to the larger ones. 

This is the theorem which provides the promised insight int 
the fundamental nature of this kind of orientation. From th 
fact that each individual unit in the process of concentratior 
selects from those others lying near it the smallest which will suf 
fice for a unit of agglomeration, there follows as a general featun 
of agglomeration the tendency not to exceed the size of a requi 
site unit of agglomeration, and hence the tendency to concentrate 
in as many centers as there exist requisite units of agglomera 




tion. This result may also be reached by showing that each ag- 
glomeration means a deviation with resultant costs; and the 
deviation which occasions these costs will not be carried farther 
than to form units which just offset these costs. However, it is 
important further to demonstrate this by making use of an exact 
and detailed analysis of the formation of the individual centers 
of agglomeration. 

d) Modifications. — We must now (again in strict accord- 
ance with our discussion of the attraction of labor locations) in- 
troduce the modification of the power of attraction of the centers 



Fig. 22 

)f agglomeration resulting from the elimination of material de- 
Dosits. This modification must be made because of the fact that 
n drawing together at one place several units of production more 
ind less favorable deposits of supply will result for each kind of 
naterial used, the respective advantages of these deposits de- 
)ending upon the relation of the supplies which were formerly 
ised by the isolated units to the new site of production. It fol- 
ows that, as in the case of the "labor locations," the unfavorable 
deposits will be eliminated (as in Fig. 22 above, M\ and M2) 
nd the supply will (assuming sufficient productivity) be limited 
p the most favorable deposits of each kind of material. 

In addition to this change, which will take place regularly, 
; may also happen that the place of agglomeration is by chance 
ituated in the neighborhood of a material deposit which has not, 


up to this time, been used. Then this new deposit will be substi- 
tuted (in place of all others of the same kind of material former- 
ly used), since it is most favorable for the new conditions of 
production. Compare Figure 23. Here M\ is eliminated as less 
favorable than Mi ; but so also are M2 and M'2 eliminated, since 
138 both are less favorable than the new deposit ikf'a- 

Both these circumstances will, by saving transportation costs, 
strengthen the power of attraction of the centers of agglomera- 
tion by a certain amount which should be added to their index of 
economy, an addition which must be the larger the farther the at- 
traction of the original index of economy happens to extend, with 
the result that more distant units are attracted and the differen- 
tial advantage between the unfavorable sources of material elim- 
inated and the favorable ones brought into use is greater. All this 
is similar to what we found in the case of labor location. 

But while the position of the attracting labor location is nol ' 
changed by ehminating certain deposits of material (since this 
labor location is definitely fixed), the effect of this eliminating j 
process goes farther in the case of agglomeration. In the lattei 
case the geographical position of the attracting place of agglom- 
eration is affected, since this position itself depends (within the 
segments of the isodapanes) upon the locational figures them- 
selves. If parts of these locational figures cease to operate ae 
effective determinants, the whole basis of orientation will be 
changed. But it may be stated at once that it is very easy to de- 
termine the new position, and that the separation from the olc 
basis is not complete; the old deposits still continue to effect 
potentially, and in a definite direction, the process of agglomera- 
tion. This last point is obvious; for the new deposits might be- 
come exhausted, and then it would be necessary to resort to thf 
old ones. 

Speaking of the new position, then, (i) the centers of con- 
sumption which are to be served from this point of agglomera- 
tion and (2 ) the sources of materials which remain in use are the 


only factors which need to be considered as the basis of a new 
locational figure with the corresponding component weights in 
order to see where the point of agglomeration will lie; it will sim- 
ply be the minimum point of the new locational figure, according 
to the laws familiar to us. In Figure 22, A is the minimum point 
of C'Mi CM' 2] in Figure 2^, A is the minimum point of C'Mi, 
CM'' 2. As is evident at once, the point of agglomeration will gen- 
erally remain in the neighborhood of the selected material de- 
posits. For numerous and divided markets which have a rela- 
tively weak attracting force will pull against material deposits 
whose weight is concentrated upon a few strong ropes (using the 
terms known to us from our Varignon apparatus). In addition, 139 
these markets will mutually paralyze each other on account of 

Fig, 24 

their necessarily opposed positions. Consequently, the original 
position of the point of agglomeration in the neighborhood of 
these (new) deposits will be retained, or at any rate will not be 
greatly changed. 


Now to turn to the usual case that, for the unit in question, 
:here is not only a saving for a certain given unit of agglomera- 
ion, but there exists also a function of economy because econ- 
omies continue to rise, increasing while the size of agglomerations 
•ncreases. Such a function of economy is in point of fact made 
ip entirely of single units of agglomeration, each one having a 
Darticular index of economy. The effects (on the distributed or 
scattered industry) of the tendency to agglomeration can be 
nade clear if one imagines this tendency to agglomeration as be- 
ng the concurrent effects of all these various units of agglomera- 
ion with their different indices. Each of these units will bring 



together the parts of the scattered industry according to the ex- 
tent of its agglomerative power, following the laws with which 
we have become acquainted. Hence we can think of their com- 
mon effect as a competition of the various units of agglomeration 
with respect to the form of the agglomeration; while within each 
of the struggling units the agglomeration takes place according 
to the rules which have already been developed. The question as 
to the effect of a function of economy composed of the units a^ a-, 
as, etc., is simply: toward which of these units will the agglomer- 
ation take place? After that question has been decided all the 
rest takes place according to the rules already set forth. 

Fig. 25 Fig. 26 

Which unit of agglomeration will win out may be deduced 
rather simply from the standpoint of the individual units of pro- 
duction affected. Around the minimal point of each individual 
unit of production extend critical isodapanes which corresponc 
to the index of economy of each unit of agglomeration. The 
critical isodapanes of the higher units with higher indices oi 
140 economy will lie more distant than those of the lower units; ir 
our example «2 will lie more distant than Gi, a^ more distant thar 
fls, etc. How this works is indicated for a function with two units 
01 and 02 in the figures below (25-28). The critical isodapanes ol 
higher units are hkely to intersect with more isodapanes of othei 
isolated units than is true of the smaller units. However, these 


higher units also need larger masses of production in order to 
come into operation; they must bring together a larger number 
of isolated units of production. And these higher units will come 
into competition with the smaller units. This may best be made 
clear by the simple example of two units of agglomeration (öi 
and Ö2) competing. 

The isodapanes of higher rank (represented in our example 
by ßo) may not bring together a larger number of productive 
units than do the lower ones, because these isodapanes are drawn 

Fig. 27 Fig. 28 

iround the minimum points at so small an additional distance 

:rom the lower ones that they do not have segments in common 

vith any more units than do those lower ones (Fig. 25). In that 

:ase the higher units of agglomeration will not be able to com- 

)ete with the lower units. Or it may be that the isodapanes of 141 

ligher rank actually include within their segments a larger num- 

)er of productive units (Fig. 2 6, where 02 includes three, and Fig. 

7, where a-, includes four, units, while öi only includes two in 

ach case). Assuming that a quantity of production sufficient 

or agglomeration is present, there will be competition between 

he two units of agglomeration. The outcome of this competition 

rill depend upon whether the ratio between the economies of 

gglomeration and additional costs of transportation is more fa- 

orable in the case of agglomeration toward Ci than it is in the 


case of agglomeration toward 02-^ This ratio is accurately ex- 
pressed by the distance between the isodapane on which the 
place of agglomeration for the unit in question will actually lie, 
and the critical isodapane belonging to this same unit. It will be 
remembered that the critical isodapane indicates the extent to 
which economies can be gained by means of agglomeration to- 
ward this unit. The isodapane on which the place of agglomera- 
tion will actually lie indicates the actual additional transporta- 
tion costs which will have to be assumed in order to effect this 
particular agglomeration. The greater the difference between 
these necessary additional costs and the actual economies, the 
more favorable the situation for agglomeration. Hence it is only 
necessary (i) to examine from the standpoint of the individual 
units of production the common segments of the critical isoda- 
pane of the different units (in our case the segments of 02 and 
öl) and (2) to ascertain in which of these segments the distance 
between the points of agglomeration and the critical isodapanes 
will be greatest in order to know in which segments the agglom- 
eration will take place. Assuming for the time being equally 
large productive units (which will place the points of agglomera- 
tion at the center of the segment), it follows that the distance 
between the points of agglomeration and th,e critical isodapanes 
142 will increase in proportion to the size of the segments. It is, then, 
only necessary to look at the size of the segments in order tc 
know toward which units the agglomeration will take place, as- 
suming that sufficient quantities of production are available for 
the segments of all the units. In Figure 26 agglomeration will 
take place toward d ; for, although it seems at a first glance pos- 
sible that agglomeration might go toward the higher unit (^2), it 
will not do so because the segments of the lower unit are larger; 
they show greater distances between the point of agglomeratioDJ 
and the critical isodapanes, and hence have greater actual econ^ 
omies. But when, as in Figure 27, isodapanes of higher rank lit 

* The text in the preceding paragraph has been rewritten. — Editor. 


so far beyond those of lower rank that not only do these higher 
isodapanes include within their segments more production (and 
sufficient production to make up the greater total quantity re- 
quired for the higher unit), but also their segments are larger 
than those of the isodapanes of lower order, then in that case the 
higher unit of agglomeration will win out. 

To sum up the argument in general terms: the agglomera- 
tion of higher rank will eliminate the agglomeration of lower 
rank only when the isodapanes of higher rank surround the min- 
imum point at a distance so much greater that they not only ( i ) 
gather within their segments the amount of production required 
for the agglomeration of higher rank, but also (2) form larger 
segments and hence offer more favorable points of agglomeration 
for the individual units of production than do the segments of 
the critical isodapanes of lower rank. 

It may, of course, be that only the critical isodapanes of ag- 
glomerative units of higher rank form segments, while those of 
lower rank do not touch each other at all (compare Fig. 28). In 
this case the agglomeration of lower rank will be unable to com- 
pete. This case is diametrically opposite to that first discussed. 
In this latter case the isodapanes of higher rank surround the 
minimum points at much greater distances than do those of the 
lower rank which cling closely to the minimum points. 


From the foregoing discussion one condition on which the 
form of the agglomeration depends should have become clear. It 143 
is the manner in which the critical isodapanes of the various 
units follow each other. According to the previous analysis, close 
succession of critical isodapanes indicates that agglomeration 
will move toward an agglomerative unit of lower rank; whereas 
wide separation indicates that it will move toward a unit of high- 
er rank; hence agglomeration depends first on the scale of the 
isodapanes. This scale presents a graphical picture of the rate 



at which the economies increase with successive units of agglom- 
eration. It is a diagram of the increase of the function of econ- 
omy — a diagram projected upon a horizontal surface (compare 
illustration below, Figs. 29 and 30). If the indices of econ- 
omy per ton of product increase rapidly as the agglomerative 
units increase, then the corresponding isodapanes (cf. a^, a.z, a^ 
in Fig. 29) are far apart. Vice versa, if these indices increase 
slowly, the isodapanes are close together (cf. a^, Go, Ö3, in Fig. 
30). The preceding analysis is thus nothing but an exact formu- 

Aj A2 A3 
Fig. 29 

Aj As Ag 
Fig. 30 

lation of the fact that (and in what manner) the size of the ag 
glomeration will be dependent on the rapid or slow increase 
the function of economy. It shows in what manner the functioi 
of economy represents the first factor influencing agglomeratioi 
by determining the number and size of the units of agglomer 

But on closer examination it shows also what additional fao 
tors are concerned. Apart from the succession of the isodapanes 
evidently three other factors must be taken into consideration! 

First, The distance according to which the critical isodz 
panes are fundamentally spaced is to be clearly understood a 
something different from their succession in the scale. A give: 
succession of critical isodapanes may be spread over a widely ex 
tended circular formation or over a narrow funnel of isodapanesj 
according to whether their basic spacing interval is large or small 
(cf. the figures of the Appendix, p. 241 f.). And each will necest 


sarily have its own significance for the agglomeration. We shall 
Dresently discuss that aspect of the matter. 144 

Second, The physical distance of the units of production. If 
they are spread widely apart, scattered about the country, the 
Dossibility of forming common segments of their isodapanes will 
De less than if these industries were already close together. 

Third, The quantity of production of the units of produc- 
:ion. On this depends the magnitude of the masses of production 
vhich are to be agglomerated within the segments, and this cir- 
:umstance determines which of the different segments, if any, 
lave access to quantities of production sufficient for their ag- 
jlomerative units. 

In analyzing these three factors further, the following ob- 
;ervations may be made. 

We are already acquainted with the first factor from our dis- 
;ussion of labor orientation. We there found that the basic dis- 
ance of the isodapanes is determined (i) by the locational 
veight of the industry (a condition implicit in its character) , and 
2) by the general rates of transportation (a general environ- 
nental condition). This first factor, therefore, may be sepa- 
ated into two conditions which work independently of each 

On the other hand, the second and third factors may be com- 
>ined, since they depend upon one single condition, that of the 
lensity of industry. For the quantity of production of the sev- 
ral units of production, taken together with their distance from 
ach other, constitute the density of industry relative to a given 
.rea. It is useful to combine these two concepts into the one con- 
ept of the density of industry, since both in reality are a reflec- 
ion of the same general environmental condition, the density of 
'opulation. Density of population empirically has these two as- 
•ects: (i) density of the population of a particular locanty= 
[uantity of production of the units of production; (2) number 



of centers of population = distribution of the individual units of 

As in the case of labor orientation, we find two conditions in- 
herent in the character of the industry, and on these two condi- 
tions the deviation to centers of agglomeration depends : ( i ) the 
junction of economy of the industry and (2) its locational 
weight. So also we have two environmental conditions : the costs 
of transportation and the density of industry (or, as we may say 
empirically, the density of population) . These are the same en 
145 vironmental conditions as those influencing labor orientation. 

Let us now first examine more closely the nature of the influ- 
ence of the locational weight and of the two environmental con- 
ditions, and second, work out at least a general picture of ag- 
glomeration under the combined influence of all the conditions j 

It will probably not be necessary to restate the general way] 
in which the locational weight and the transportation costs worL 
It will be remembered that if both decrease, the isodapane will 
expand; if both increase, the isodapane will tend to contract — 
in other words, both factors work alike. It is more important to 
realize that one of the two factors upon which the density of m-\ 
dustry depends, namely, the distance of the individual units 0) 
production, has the same effect. The expansion or contractioi 
of the isodapanes (without altering their order in the scale, to be 
sure) as caused by a change of locational weight and a change ol 
transportation costs (or either one of these causes) amounts to 
an augmentation or diminution of the sets of isodapanes. Such 
expansions or contractions will therefore increase the number oi 
points at which isodapanes intersect, just as bringing the sets oi l 
isodapanes nearer together without altering the size of each indi-j ^" 
vidual isodapane will increase the number of intersections. It is 
therefore permissible to regard locational weight, transportationj 
costs, and distance of the units of production from one another 
— to regard all of them as a sort of similar mode of influence 
which is uniform in its effect. 


What does this expansion of unaltered sets of isodapanes 
mean with respect to the formation of segments, and therefore 
with respect to the scale of agglomeration? To begin with, it 
clearly does not mean the same thing as an alteration of the 
order of the isodapanes in the scale — an alteration which results 
from changes in the function of economy. The expansion of 
unaltered sets of isodapanes must not be confused with an alter- 
ation of the order of the isodapanes in the scale. But, as in the 
latter case a further extension of the higher isodapanes means 
facilitating some agglomerations, so bringing the sets nearer to- 

FiG. 31 Fig. 32 

igether will have the same effect; because such an approach ob- 146 
! viously increases the segments and aids in piling up sufficiently 
'large quantities of production within the segments; in other 
words, the two decisive factors are influenced favorably, and 
it will cause agglomeration to take place on a larger ''scale." 
"This will be evident from the above figures, which are simplified 
by showing a function of economy with only two stages (öi and 
a.). The distance of the isodapanes (that is, the function of 
economy) is precisely the same in Figures 31 and 32 ; the figures 
differ only in the distance between the units of production. In 
Figure 3 1 the distance between the units is greater than in Fig- 
ure 32, where they have been brought nearer together by one 
quarter. In Figure 3 1 there may be agglomeration only toward 


Ö1, and even this only on the assumption that two individual in- 
dustrial units will suffice to make up the required quantity of 
production. In Figure 32, however, there are (due to the smaller 
distances of the units of production) possibilities for agglomer- 
ation toward a^ and Ö2, if we assume that the total quantity of 
production of all four units of production is necessary and suf- 
ficient to make up the required quantity for a.. Under that as- 
sumption the agglomeration will, in fact, take place in the direc- 
tion of the higher unit a^, since the distance between the critical 
isodapane and the midpoint of the segment (point of agglomera- 
tion) is greater for 02 than for ax. To sum up: bringing the sets 
of isodapanes nearer together affects the "scale" of agglom- 
eration. It affects the scale of agglomeration less than varying 
the function of economy affects it; for if I draw the locational 
figures a given distance toward one another all isodapanes, in- 
cluding those of lower order, come nearer together. The gross 
economy, therefore, increases at every step in the scale, but more 
rapidly in the higher order than in the lower order. If, however, 
I affect only the rate of succession in the scale — if, in other 
words, I let the isodapanes of higher order extend farther, then 
only these isodapanes of higher order within the different sets of 
isodapanes approach one another and the gross economy of ag- 
147 glomeration increases only with respect to them. The scale of 
agglomeration will therefore be much more immediately affected. 
Later it will be our task to formulate more precisely the differ- 
ence in the measure of effectiveness of the various factors. In the 
meantime this indication of their different ways of working must 

We now come to consider the second part of the third fac- 
tor : the quantity of production of the units of production. We 
can only say of this that an increase of it quite obviously facili- 
tates agglomeration, increases its "scale"; while a decrease di- 
minishes it. For if the quantity of production in the individual 
industries increases sufficiently, the common segments of less 


widely extended isodapanes will now contain the quantity of 
production requisite for a unit of agglomeration. Similarly, sets 
of isodapanes which formerly did not have the requisite quanti- 
ties in common segments of their higher isodapanes will now 
possess them. The unit of production may even "by itself" gain 
so much weight that it represents various degrees of the function 
of economy even without concentration; and one may imagine 
the extreme case in which a whole function of economy is real- 
ized through increasing the quantities of production of the unit 
of production without the industry necessarily being deviated. 
This may suffice to indicate the basic effects of the quantity of 
production upon agglomeration. It is impossible to give more 
than this elementary idea here; for the locational figures and 
their isodapanes fail us as graphic aids in clarifying issues in- 
volving the quantities of production of the units of production. 


It is, however, possible to get farther by other means in 
our attempt to explain the significance of all the factors taken 
together. It is possible to arrive analytically at a precise formu- 
lation of the degree of influence of the various factors by assum- 
ing that industries are distributed evenly and produce every- 
where the same commodity. We may thus get for the entire 
industry an insight into the orientation which results from every 
combination of the factors. This is accomplished by the formu- 
la of agglomeration as set forth in the Appendix.^ But it is im- 148 
portant to keep in mind the assumption of uniform density of 
industry throughout a given area, an assumption which will not 
be vaHd for any actual industry or any actual country. The for- 
mula, so far as it gives us the number and size of the centers of 
agglomeration arising from any combination of the various fac- 
tors, has, therefore, only a theoretical value. It gives only a gen- 
eral idea (probably rather far removed from reality) with which 

^ Cf . p. 246 f., infra. — Editor. 


we can compare the reality without necessarily expecting to rec- 
ognize in the reality the picture set up by the formula. The for- 
mula is in this respect only an aid to understanding. But that is 
only one aspect of it. The formula is no doubt more important in 
so far as it enables us to ascertain with precision the effect which 
changes in any one of the factors of agglomeration will have 
upon the agglomeration as a whole. And this service our formula 
does render, not only theoretically, but also for any given case. 
Because no matter how many different degrees of density are ac- 
tually to be found for a given industry in different localities, the 
factors in question must be operative in each of these localities i 
(and consequently in the whole body of that industry) accord- 
ing to the same relative degree of influence which they would 
have in an industry distributed smoothly and evenly. Such 
even distribution of industry merely represents one of the vari- 
ous grades of density of the real body of industry. 

Let us attempt to clarify the result which has been attained 
in the Appendix and translate its formulas into non-technical lan- 
guage. Up to this time we have dealt only with the absolute 
economies which could be attained per ton of product in each 
stage of agglomeration. These economies were treated as a func- 
tion of the size of the agglomeration, the concept "function oi 
economy" being utilized. One may, however, according to the 
Appendix, inquire into the relative increase of economies which 
takes place as there is an increase in the size of the agglomera- 
tion, i.e., the increase of economy which, starting from any given 
stage of agglomeration, is attained by the addition of anothei 
industrial unit. And since this increase of economy depends 
solely upon the stage of agglomeration already reached — if we! 
imagine the small units as small enough in comparison to the 
large ones which attract them — we shall recognize a second func 
tion which expresses the power of attraction of the various stages 
of agglomeration. This second function is called in the Appen 
149 dix the ''function of agglomeration." The function of agglom 


eration f(M) is composed of the additional saving which cor- 
responds to each step of progress from one stage of agglomera- 
tion to another. In the Appendix the relation of this function of 
agglomeration to the function of economy (with which we have 
previously dealt) is analyzed; it is shown that the two functions 
are intimately connected, and it is shown in what manner they 
are connected. 

All that concerns us at the present time is the fact that the 
function of agglomeration expresses with precision the power of 
attraction which a large unit of industry exercises over scat- 
tered smaller units. As the equation (Bestimmungsgleichung) 
for the extent to which a large unit attracts smaller units, we get 

the formula R=^ ~\'^ ^^ which R is the radius of agglomeration 

as extended, A the locational weight of the industry, and s the 
transport rate which prevails. Thus we find that the attraction 
of a large unit of industry is directly proportional to the value of 
the function of agglomeration, and inversely proportional to the 
locational weight of the industry and the prevailing transport 

So much for the relevance of these three factors of agglom- 
eration. If we wish to get an insight into the actual extension of 
the radii of agglomeration and to determine the actual amount 
of agglomeration it is necessary to take into account the thus- 
far neglected fourth factor of agglomeration, the ''density of in- 
dustry." The density of industry ( p ) determines the length of 
the radius (R) which is necessary in order to bring together any 
given quality of agglomeration (M). The formula is as follows: 

M = TrR'p, 



If we introduce this value into the equation of agglomeration, 
instead of the unknown radius of agglomeration, R, we get: 

M AM) 


Trp AS 

150 or 


V TTp 

The meaning of this formula may be interpreted as follows: As- 
suming that the locational weight of an industry {A), the rate 
level(5), and the density of industry (p) are known, we must in- 
sert into the formula that value of (M), i.e., that magnitude of 


agglomeration with which some value of /(ikf)=— 7= V Mi i^ 

V TTp 

we wish to know which of the possible values of a function of ag- 
glomeration j{M) of an industry will become effective, or, in 
other words, if we wish to know what ''scale" of agglomeration 
will actually become a factor for an industry when the conditions 
of agglomeration are known. This formula solves the problem. 
The Appendix shows in a simple manner how one may deter- 
mine by diagram whether an effective M, which corresponds to 
these conditions, exists at all, and therefore whether any ag- 
glomeration will take place. It shows also how we can deter- 
mine the value of M. The Appendix brings out further that if 
we know the size of the individual units of agglomeration we also 
know the number of centers of agglomeration which will arise in 
any area with a known total production. We get the number of 
centers of agglomeration by dividing the total quantity (G) by 
the value of the single agglomerations. 


What has been considered up to this point has applications 
to the influence of the forces of agglomeration upon industries 
oriented at the points of minimum costs of transportation. What 



will be the result if the forces of agglomeration are considered 
for industries oriented at the labor locations ? 

In order to analyze what happens in this case we shall do 
well to bear in mind that labor orientation is one form of devia- 
tion from the minimum point ; agglomeration is another. When 
agglomerative forces appear in an industry oriented toward la- 
bor, there takes place a competition between the agglomerative 
deviation and the labor deviation, a struggle to create "locations 
of agglomeration,"*^ as compared with "labor locations," both be- 
ing upon the foundations of the transportational groundwork. 151 
That one of the two forces which can offer the greater net econ- 
omies over and above the transport orientation will be the victor. 

It might at first thought be held that if we are to consider 
pure competition between agglom-locations and labor locations 
we should simply compare the net economies of agglomeration 
with the net economies of labor. But this is not the correct plan 
of attack, for a labor location may, and, as we already know, in 
most cases will, itself be a point of agglomeration — accidental 
agglomeration, we have called it. In connection with this acci- 
dental agglomeration economies of agglomeration will occur, and 
these economies will be precisely in accord with that measure of 
the function of economy which the agglomeration, according to 
its size, represents. These economies of agglomeration are sep- 
arate and distinct from the economies of labor which attract in- 
dustry toward that particular labor location. These economies 
Df accidental agglomeration must therefore be added to the econ- 
Dmies of labor if we wish to know the total amount of economies 
with which the labor locations compete with the purely transpor- 
:tational locations of agglomeration. The question then is. Which 
is larger, the economies of agglomeration at such agglom-loca- 
tions, or the economies of labor plus the economies of accidental 
agglomeration at the labor locations? 

^ Hereafter occasionally referred to, for brevity's sake, as "agglom-locations." 



That means that all industries in the case of which acciden- 
tal agglomeration at labor locations creates units of agglomera- 
tion as great as, or greater than, pure and independent agglom- 
eration within the groundwork of transport orientation retain 
their labor orientation. For in such a case the economies due tc 
this accidental agglomeration are greater than those which the 
agglom-locations can offer. Only those industries in the case o: 
which the accidental agglomeration creates smaller units of agi 
glomeration can possibly be otherwise oriented. But this wil 
happen only when the loss of economies of agglomeration (re* 
suiting from the smallness of the unit) is not compensated foj 
by the economies of labor which are offered by the labor lo^ 

It is necessary to keep two things in mind: First, Industrie« 
with a highly developed labor orientation have a selection of la 
bor locations due to the competition of such locations with oi 
another. This very process of selection causes a considerabl 
152 accidental agglomeration at the more favorable labor locations; 
labor orientation itself shows a tendency to agglomerate. Seq 
ond, the strength of this tendency to agglomerate depends upo 
three of the four factors upon which the strength of the inde 
pendent tendency toward agglomeration depends. Locations 
weight, rates of transportation, and density of population affec 
labor orientation and its accompanying accidental agglomeratio 
in the same way and just as much as they affect the competin 
independent or pure agglomeration. Consequently the fourti 
factor must differ very greatly indeed if it is to prevent the aco 
dental agglomerations due to labor orientation from being s 
large that (with their economies of labor added) they do nc 
overcome the independent agglomerations. Thus only Industrie 
which have a very high function of economy and a very wea 
labor orientation (and therefore very small accidental agglorr 
erations at the labor locations) can be subject to a successfi 
competition by pure and independent agglomeration. Indepenc 



ent agglomeration within the groundwork of transport orienta- 
tion will not eliminate possible labor orientation in any large 
proportion of industry. 

On the contrary, the addition of economies of agglomeration 
to labor economies will in important sections of industry (name- 
ly, in all cases in which a large agglomeration is due to labor ori- 
entation) strengthen labor orientation as compared with trans- 
port orientation. For wherever the accidental agglomerations 
caused by the labor locations are larger than any possible inde- 
pendent agglomerations within the groundwork of transport ori- 
entation, the balance between the two is added to the economies 
of the labor location as an economy not otherwise to be attained, 
and this strengthens the power of attraction of the labor loca- 
tion. 153 

We can make clear the significance of these influences by 
the following example, chosen quite at random: Let us examine 
the effect of the following function of economy for a series of 
different industries: 

No. of tons . . 100 200 300 400 500 600 700 800 
per ton. . . i 4 6 7 7.5 7.75 7.82 7.88 

What will be the effect of these economies of agglomeration 
in industries with labor costs of $10, $50, $100, $200, $300 per 
ton of product? Let us suppose that the labor economies at the 
labor locations amount everjrwhere to 10 per cent. Let us sup- 
pose further that the accidental agglomerations which occur in 
consequence of labor orientation amount to 50, 100, 200, 400, 
800 tons. The unit of independent agglomeration within the 
groundwork of transport orientation which can be attained in 
accordance with the aforementioned function of economy is, of 
course, the same in all the industries. Let us say it is 300 tons. 

Then Table I will show how ''independent agglomeration" 
and ''labor orientation" compare with each other for the various 



We find three groups of industries: First, there are indus- 
tries with a very small index of labor costs (of less than $50 per 
ton of product, Group i ) in which labor orientation is in itself 
so weak that it can only cause small deviations and concentra- 
tions. In this case we find a superiority of the independent ag- 
glomeration with its larger units of agglomeration and greater 
economies (5:1); such a state of affairs leads to orientation to- 
ward agglom-locations within the groundwork of transport ori- 
entation. However, such a type of change in location cannot- 


A. Labor Orientation 

B. Agglomeration 

C. Extent 
to Which 

Economies op 
A Exceed 

Those of B 

Labor Cost 
perT. P.* 

per T. P. 

Unit of 
tion (tons) 

per T. P. 

Unit of 
tion (tons) 

per T. P. 


Group I 

Group II. . . 

Group III. . 














- 4 

+ I 
+ 9 
+ 22 
+32.8 i 

*T. P. = ton of product. i 


bring with it any considerable movement, since industries which 

are subject to it have only been slightly deviated anyway. Foi 

that reason the movements of this group of industries cannot 

154 have very great practical significance. 

Second, there are industries in which the units of independ 
ent agglomeration are larger, to be sure, than the units of ag^j 
glomeration due to labor orientation (300 as compared with loc! 
and 200 tons. Group II). But the addition of these economies of 
accidental agglomeration to the labor economies make the totaii 
economies due to labor orientation larger than the economies 
due to independent agglomeration within the groundwork oi 
transport orientation. Consequently the orientation toward la- 
bor locations takes place. (The ratios of economies are 6: 5 andi 


And third, there are industries in which the units of agglom- 
eration at labor locations are larger than those of the independ- 
ent agglomeration (400 and 800 as compared with 300), and in 
which the addition of the economies of agglomeration cannot 
but strengthen the influence of the labor orientation. But grant- 
ed that these additional economies (due to accidental agglom- 
eration at the labor locations) strengthen labor orientation in 
general, how will they affect these industries within the ground- 
.work of labor orientation? 

I In general we may say that they will lengthen the radius of 
attraction of the labor locations in much the same way as do the 
additional transport economies resulting from the replacement 
of material deposits (cf. supra, p. 113). We can measure the at- 
tracting power of each individual labor location only if we add 
to the labor economies which it offers, not only those economies 
resulting from the replacement of deposits, but also all the econ- 
omies of accidental agglomeration which result from the total 
amount of production attracted. 

This will mean, for the final orientation of the industry, 
(irst, that particles of the industry which would otherwise have 
remained oriented at the points of minimum cost of transporta- 
tion will be deviated to the labor locations. Due to the addi- 
tional economies of accidental agglomeration, labor orientation 
2S a whole will prevail over transport orientation where it would 
lot otherwise prevail. And it will mean, second, that within the 
labor orientation of the industries the strong labor locations 
(which by virtue of the large percentages of "cost reduction" 
which they can offer have already attracted the weaker ones to 
hemselves) get a further ''advantage," because the amount of 
Droduction agglomerated in them represents units of agglomera- 
:ion having economies of agglomeration. The radius of their at- 155 
Taction will consequently be further extended, and they will at- 
:ract the production of weaker locations still farther away. The 
strength of labor orientation itself will be still more accentuated. 



The essential effect which the tendencies to agglomeration 
will have on labor orientation is to increase its inherent tenden- 
cies toward concentration at a few locations. 




If we now attempt to fit the results of the preceding para- 
graphs into the actual development of our economic system we 
do so because we wish to make the meaning of these results a bit 
more clear. But we are not concerned with an inductive verifica- 
tion of these results. 


For this purpose, and only for this purpose, we undertake 
to discuss the question: upon w^hat qualities of a particular in- 
dustry does the amount of its agglomeration depend, a questioi 
which we had eliminated for methodological reasons. This ques 
tion causes us to examine more carefully those conditions of ag 
glomeration which depend upon the nature of the particula 

There are two such conditions: the locational weight anc 
the function of economy. Of these, the locational weight is i 
simple and obvious characteristic of every industry, and it con 
tains no problem. We need not stop to discuss it. 

But the function of economy is another matter. It is no 
something visible and tangible, but something quite indefinite 
in its way it is merely the product of certain other, more deepb 
rooted characteristics of each industry. We cannot know by de 
duction upon which characteristics of a given industry this func 
tion of economy depends, and we cannot know by deduction hov 
it depends upon them. Nor would it enable us to determine thesi 
characteristics more fully if we could render more explicit thi 
mode by which this function of economy has been created, a; 



has been attempted in the section entitled ''Agglomerative Fac- 
tors." To be sure, it is manifest that there is a connection be- 156 
tween the function of economy, the agglomerative factors by 
which this function is created, and the character of the different 
industries; moreover, it is manifest that the two most essential 
groups of agglomerative factors (namely, the development of 
the labor organization and the development of the technical ap- 
paratus of each industry) will create a varying function of econ- 
omy with varying units of agglomeration. But we cannot de- 
duce definite rules which state what qualities of a given industry 
will determine the size of the units of agglomeration and their 
succession, in short, the shape of the function of economy.^ 

If we would secure a general idea of the function of econ- 
omy and if we would understand its relation to the character of 
industries we must start from quite another consideration. Only 
industries with products whose value is to a large degree a result 
Df the industrial (or formative) process itself can possibly have 
ilarge units of agglomeration with resultant high percentages of 
compressible^ costs — an effective function of economy. We may 
5ay that such industries show a high "value added through man- 
ifacture" (Formwert) }° The reason why only industries with 
juch a high value added through manufacture will have an effec- 
;ive function of economy is simple. We know it already from the 
malogous reasoning about the labor value and the index of labor 
:ost.^^ There we said that only where high labor costs per ton of 
oroduct exist can considerable labor economies per ton of prod- 
ict be effected; and the same consideration holds good for man- 

^ Cf . here the Mathematical Appendix, below. — Editor. 

^ Cf. supra, p. 106, — Editor. 

" The meaning of this term Formivert is best rendered by "value added by 
Qanufacture." But since manufacturing is the process of giving "form" to coarse 
Qaterials, "form-value" may not be an impossible term. A. Predöhl uses it. Cf. 
'ournal of Political Economy, XXXVI, 371 ff. Moreover, there is the already 
stablished term form-utility. — Editor. 

" Cf. supra, p. 107. 


ufacturing costs in general, including the costs of machinery, etc. 
These manufacturing costs, speaking generally, appear in the 
value added through manufacture of a product. They can show 
high indices of economy through high percentages of compressi- 
bility, only provided the costs themselves are high. These gener- 
al manufacturing costs are the very ones which the effective elab- 
oration of the working force and of the technical apparatus (the 
two most important groups of agglomerative factors) tend to re- 
duce. They represent the most essential object of cost reduction 
through agglomeration. But even the elaboration of the working 
force and of the technical apparatus creates, first, large units of 
agglomeration, and second, high percentages of compression of 
the large units as compared with the small units ; these two devel- 
opments will be of moment for the orientation of an industry 
only provided the value added through manufacture of that in- 
dustry per ton of its product is high. We shall call this value add- 
ed through manufacture per ton of product the index of value 
added through manufacture of that particular industry or simplj 
157 index of manufacture. If that index rises, equal percentages o} 
cost reduction of equal units represent greater economies per tor 
of product, and the corresponding critical isodapanes of the loca- 
tional figures will be farther extended, the attracting force of tht 
unit of agglomeration will increase, etc. 

To the extent to which this index of value added througl 
manufacture is the object of all attempts to reduce cost througl: 
agglomeration — and we have noted that the two most importanii 
groups of agglomerative factors work in that way — this indej 
affords us a rod for measuring the effective tendency toward ag-; 
glomeration of industries. It must be said, however, that this 
measuring rod does not tell us anything final concerning the ac 
tual trend toward agglomeration of a particular industry, and ii 
does not tell us its actual function of economy; it only outlines 
the effective tendency toward agglomeration. For this measur- 
ing rod does not point out which reductions exist in reality (duti j. 


to the elaboration of the working force and of technical appa- 
ratus) , nor does it tell what is the order of succession of the units 
of agglomeration. But since we do not have clear knowledge 
concerning the dependence of the function of economy and of 
the virtual agglomeration of industries upon the general charac- 
ter of these industries, we may just as well use the measuring 
rod which is at hand. This being true, we shall do well to ex- 
amine this index of value added through manufacture a bit more 
carefully, and to relate it to the second general characteristic of 
the industries, their locational weight. 

The value added through manufacture of an industry has two 
main constituent factors: the labor costs expressed in wages 
and salaries, and the costs of machinery, the latter to be inter- 
preted in their widest sense, as including interest and amortiza- 
tion of fixed capital and cost of power. We shall distinguish 
these two as "value added through labor" and ''value added 
through machines." Now it is of the greatest importance (if we 
are to use the index of manufacture as a measuring rod of ag- 
glomeration) to know in what proportion those two factors enter 
into that index. To the extent to which the value added through 
manufacture results from machines, a factor curbing agglomera- 
tion appears. This factor is the increasing use of fuel, which 
means a rising material index of the particular industry. We can 158 
say that value added through labor is a pure factor of agglomer- 
ation, while the factor of value added through machines is to a 
large extent paralyzed by a rising material index. This fact does 
not prevent us from using the value added through manufacture 
of an industry as a virtual measuring rod of its agglomeration, if 
only we do not forget to take into equal consideration the second 
measuring rod which is contained in the material index and the 
locational weight. This necessity of keeping both rods in mind 
suggests that we relate the notion of the value added through 
manufacture to that of the locational weight and create a con- 
necting concept out of the index of manufacture and of the loca- 


tional weight, just as we have previously done in the case of the 
index of labor costs and of locational weight for our analysis of 
labor orientation/- This is possible by relating the index of man- 
ufacture, not to the ton of product, but to the total weight which 
has to be transported — the ' 'locational ton." In analogy to the 
term "labor coefficient" used earlier, we shall suggest the term 
''coefficient of manufacture" in order to describe the value added 
through manufacture per locational ton. Now we can formulate: 
industries with high coefficient of manufacture show strong tend- i 
encies to agglomerate; industries with low coefficient of manu- 
facture show weak tendencies to agglomerate ; and these tend- 
encies are inherent in their nature. This formula is comparative- 
ly simple, but it must be remembered that a considerable number 
of assumptions have been made in the process of constructing it. 


Let us ask next what will be the practical consequences oi 
this agglomeration whose general rules we have just outlined anc* 
whose underlying forces we have characterized in detail. Ir 
what forms shall we find it in reality? 

It will be remembered that agglomeration may influence 
both transport-oriented industries and labor-oriented industries 
It influences labor-oriented industries simply by increasing theii 
contraction of labor locations (according to rules we have al 
ready discussed) . Only industries with a very weak tendency tc 
labor orientation show pure and independent orientation withir 
J (-Q the groundwork of transport orientation instead of showing la« 
bor orientation. 

It will also be remembered that considerable technical ag 
glomeration occurs only in connection with a high coefficient o: 
manufacture, and this coefficient is composed of value addec 
through labor and through machines. But since value addec 

^ Cf. supra, p. no. — Editor. 




through machines is always connected with considerable con- 
sumption of material (coal), such value can hardly cause the co- 
efficient to be a high one on account of the resulting high loca- 
tional weight, unless a considerable increase in the consumption 
of human labor (value added through labor) occurs at the same 
time. Consequently industries with a high coefficient of labor will 
show the strongest tendencies of agglomeration — as long and in 
so far as machines mean considerable consumption of material. 
But these industries are strongly labor-oriented and therefore 
already agglomerated. 

The main consequence of technical agglomeration will, un- 
der present conditions, be found to be a strengthening of labor 
orientation. The other consequence, that of altering the trans- 
port orientation by creating independent agglomerations, is in- 
significant in comparison. For in the case of this latter conse- 
quence the agglomerating tendency operates generally with a 
low coefficient of manufacture, and is therefore itself not as 
strong as in labor-oriented industries. 

Two results follow which are important for our examination 
of reality later on: 

First, we shall find the transport-oriented industries some- 
what concentrated, and concentrated not very far away from 
their points of smallest costs of transportation. 

Second, wherever we encounter an industry which deviates 
considerably from its transport orientation we shall be safe in 
assuming, in case of doubt, that it is an industry oriented toward 
labor. These results will considerably facilitate our later analy- 
sis of the facts, for they enable us to separate industries into two 
great groups: transport-oriented and labor-oriented industries. 
This makes it possible for us to approach reality, bearing in 
mind the simple issue upon which this distinction is based, and 
to neglect (at least in preliminary studies) all more detailed dis- 
tinctions. 160 



Which tendencies of development shall we find upon closer 
examination to operate upon agglomeration in actual life? We 
know the different conditions of agglomeration from our analy- 
sis ; they are density of population, rates of transportation, and 
coefficient of manufacture. 

The tendencies and the significance of the first two condi- 
tions are clear. It is obvious that rising density of population 
and declining costs of transportation are evolutionary trends of 
modem times. They of necessity continuously increase agglom- 
eration. The critical isodapanes of the locational figures are in- 
cessantly extended by declining costs of transportation, and this 
creates effective segments of higher units of agglomeration; 
quantities of production sufficient for higher units of agglom- 
eration are incessantly created by the increasing density of the 
population, and this at the same time pushes the locational fig- 
ures closer together. It is hardly necessary, therefore, to take 
more time and space for the discussion of these tendencies of de- 

But the significance of a change in the conditions which are 
deeply rooted in the general character of a given industry is not 
quite as obvious. Such deep-rooted conditions are implied by the 
coefficient of manufacture, which contains value added through 
manufacture and locational weight. These conditions also lead 
in the direction of agglomeration, but not without certain curbing 
influences becoming effective. 

On the one hand the value added through manufacture be- 
comes a cause of considerable agglomeration. For the elabora- 
tion of the working force and of technical apparatus during the 
eighteenth and nineteenth centuries meant, as is well known, 
the creation of increasingly large frameworks of industrial pro- 
duction. It meant, consequently, the creation of higher units 
of agglomeration and of more extensive reductions (compres- 
sions) of the index of manufacture of various industries in cases 


in which these higher units of agglomeration become effective. 
To express these observations in the terms of our theory, this de- 
velopment of organization and technique has given to the value 
added through manufacture of the various industries that signif- 
icance which it was necessary for it to have if it was to be utilized 
in the creation of those high and effective units of agglomeration 
under whose influence these industries have been ever since. In 
this way the development of organization and technique has 
doubtless had an enormous agglomerative effect. 161 

On the other hand this development has caused forces to ap- 
pear which curb these agglomerative tendencies. It has done so 
by its influence upon the consumption of materials, which con- 
sumption in turn influences the locational weight. The creation 
of those new big frameworks of industrial production has meant 
to a large extent the replacement of manual labor by mechanical 
apparatus, and it has meant the replacement of value added 
through labor by value added through machines. In consequence 
of all this the weights which must be moved for production are 
increased, the isodapanes around the locational figures are con- 
tracted, and there is an increase of the resistance which the high 
units of agglomeration have to overcome in order to come into 
existence at all. 

The tendencies of modern development have, on the one 
hand, given to the coefficient of manufacture a considerably in- 
creased significance so far as agglomeration is concerned; but 
they have, on the other hand, reduced the revolutionary effect of 
these new units of agglomeration by reducing this same coeffi- 
cient of manufacture (due to a process of "materiahzation" of 

We must keep all these facts in mind if we would understand 
the part played by agglomerating tendencies in the industrial 
revolution of the eighteenth and nineteenth centuries. It is ob- 
vious from the viewpoint of this part of our theory that the 
change from handicraft to factory production (which consti- 


tutes the most important aspect of this revolution) is a gigantic 
process of agglomeration. Previous to this development even 
those parts of production which (due to high coefficients of manu- 
facture) were in themselves capable of considerable agglomera- 
tion had remained distributed in individual producing units, 
which were mostly situated at the places of consumption, be- 
cause of the low prevailing material index, as has been pointed 
162 out. For all these industries the discovery of the fact that their 
index of manufacture was capable of great reductions within 
new, highly developed frameworks of production meant their 
gradual readjustment — the revolution before referred to. This 
revolution does not appear in its full severity until the rapid 
rise of population is accompanied by an equally rapid decline 
of the transportation rates during the nineteenth century. But 
what will take the place of the old crafts, how far agglomera- 
tion will extend, what magnitude of agglomerative units will be 
developed, at what points the centers of agglomeration will be 
fixed — all these matters depend quite considerably upon how the 
material index of industries is changed by the development of 
technique and organization in these industries. In other words, 
these matters depend upon to what extent their locational weight 
increases and their coefficient of manufacture decreases ; to what 
extent the coal deposits enter in ; and how far the otherwise pre- 
vailing agglomeration at the most advantageous labor locations 
will thus be interfered with by an agglomeration resting upon | 
transport orientation. All these problems appear in reality as a 
competition of the labor locations with the coal deposits. The 
outcome is a selection of the labor locations, with, however, some 
attention to their proximity to coal deposits. But the inductive 
part^^ will show that we have usually overestimated the extent 
to which agglomeration at the coal deposits was necessary; by 

"Not published. Cf. instead Alfred Weber's contribution to the Grundriss 
der Sozialökonomik, Vol. VI, "Industrielle Standortslehre (Allgemeine und kapi- 
talistische Theorie des Standortes)." — Editor. 


far the more important part of the effectiveness of modern ag- 
glomerative units was the increased concentration of industries 
at the labor locations, and this was coming anyway. It will also 
show that the concentration of industries at the coal deposits 
represents to a large extent a reorientation of industries which 
had already been oriented toward material deposits; it is true 
that they were different and more widely distributed deposits. 
All this agglomeration is accidental from the point of our theory; 
it is not technically necessary. Still, we shall find to how large 
an extent the new agglomeration at favorable labor locations has 
been influenced by the increased emphasis upon the material 
aspect of production, and how this fact has influenced, not only 
the emergence of the attracting labor locations, but also the ex- 
tent of agglomeration at these labor locations. It will become 
apparent in this connection that only those industries have 
reached the highest stages of ''technical" agglomeration in which 
the change of the proportion between value added through ma- 
chines and value added through labor does not exceed a certain 
maximum. 163 

But particularly will this inductive treatment" show that 
the problem of agglomeration is not exhausted by treating that 
accidental agglomeration at extensive material deposits, partic- 
ularly coal deposits, and not even by treating that technically 
necessary agglomeration at labor locations ; there exist over and 
above these considerations, and exceeding them by far, kinds of 
''social agglomeration." This type of agglomeration develops at 
the labor locations (largely without any technical necessity) 
• upon the foundation of certain rules of agglomeration of human 
labor. It will be one of the main tasks of the inductive treat- 
ment just referred to to show, first, in which particular way this 
social agglomeration with its creation of industrial and metro- 
politan districts develops on top of the simpler and more limited 

" Cf . the last footnote. — Editor. 


forms of agglomeration which we have analyzed in the forego- 
ing paragraphs. We shall need to show, second, that this type of 
agglomeration does not evolve from causes which belong to a 
system of "pure" economics (which we have discussed previ- 
ously) but that it is the consequence of quite different factors 
which are rooted in the particular social structure of the modern 
economic system. This type of agglomeration may disappear if 
164 the social structure to which it belongs disappears. ^^ 

^^ This point is more or less well brought out by a number of monographs 
published since Alfred Weber's theory appeared. Cf. the series of studies edited 
by himself, Alfred Weber, Ueber den Standort der Industrien II. Teil: Die 
deutsche Industrie seit i860 beginning with Otto Schlier, "Der deutsche Industrie- 
körper seit i860" (1922). For an analysis of recent changes Edgar Salin, "Stan- 
dortsverschiebungen der deutschen Volkswirtschaft" (in: Strukturwandlungen 
der deutschen Volkswirtschaft [1928] edited by Bernhard Harms) should be con- 
sulted. Particularly interesting to the American student are two recent mono- 
graphs by Andreas Predöhl in the Weltwirtschaftliches Archiv, "Die Standorte 
der amerikanischen Eisen- und Stahlindustrie" (1928) and "Die Südwanderung 
der amerikanischen Baumwollindustrie" (1929). Finally attention may be called 
to Hans Ritschl, "Reine und historische Dynamik des Standorts der Erzeugungs- 
zweige" in Schmollers Jahrbuch (1927), and Joh. J. Haurath, "Zum Problem der 
hypothetischen und konkreten Standortsbedingungen. Dargelegt am Beispiel dei 
Grosschlachterei in den Niederlanden," in Weltwirtschaftliches Archiv (1926).— 



We have so far built up our theory on the assumption that 
the activity connected with the productive and distributive proc- 
ess of an industry is a uniform and indivisible thing which can 
only as a whole be drawn to and from the material deposits and 
the place of consumption by locational forces, and which goes 
on entirely independent of the activities of other industries. But 
this indivisibility of the productive process and its independence 
of the productive processes of other industries do not in fact 

We must now take the following facts into account: First, 
the productive process of almost every industry consists of 
diverse parts, which are technically independent of one another 
and can, therefore, be undertaken at different places. We may 
well think of the productive process as a heap of little balls which 
have been rolled together at one place by the (dynamics of the) 
-ocational factors we have discussed, but which may be redis- 
:ributed by those factors. Second, the forces which move those 
ittle balls (those parts of the productive process) are not con- 
iined within a particular productive process ; rather they are as- 
Dects of a complex of larger forces resulting from the intertwin- 
ng of the different parts of industrial production of a country. 
Ve shall designate the first set of facts as the organization of the 
tages of a given productive process or enterprise (Produktions- 
tuf engliederung), and the second set as the interlacing (Inein- 
nder greif en) of the independent productive processes. 165 








Let us suppose that an industry is influenced only by cost of 
transportation, and let us neglect all the deviating influence of 
labor and agglomeration. What, given such assumptions, does it 
mean that the productive process does not need to be entirely 
performed at one location, but may be split into a number of 
parts which may be completed at different locations? 

The only cause which could lead to an actual split and to a 
resultant transfer of the parts to different locations would ob- 
viously be that some ton-miles would be saved in the process. 
For the reduction of these ton-miles to a minimum is the sole 
principle regulating transport orientation — the principle which 
produces the locations we have previously discussed. We must 
accordingly consider whether the ton-miles^ are lowered if the 
locations of the stages or parts of production are separated. li 
we find that they are lowered, we shall need to determine where 
the transport locations of the split industry will be situated. 

Let us take a simple case, an enterprise with three materia 
deposits and one which is capable of being split, technologicall} 
speaking, into two stages. In the first stage two materials arc 
combined into a half -finished product {Halbfabrikat) ; in thi 
second stage this half-finished product is combined with tht 
1 66 third material into the final product. Figure 33 shows where the 
location P of the unspHt production would be situated according 
to our earlier locational rules, assuming certain proportions oi 
the weight of materials outside and inside the final product. Lei. 

^ We shall have to imagine these ton-miles as permeating the entire produc-i 
tive process, of course. ' 



us suppose that possible locations of the split production would 
be in Pi and P2 ; Pi for the first stage and P2 for the second stage. 
What will be the result if the splitting occurs? Obviously, we 
shall have two locational figures with three roots instead of one 
figure with four roots. The first locational figure is M1M2P2; 
it is rooted in the two material deposits of the first stage of pro- 
duction and the place of production of the second stage of pro- 
duction which is also, obviously enough, the place of consump- 
tion of the first stage. The second locational figure is M^PiC; 

Fig. 33 

it is rooted in the place of production of the first stage, and in the 
location of the additional material deposits, and in the place of 
consumption of the final product. Pi, the location of the first 
stage of production is the point of minimum costs of transporta- 
tion,^ or the minimum point, as we have called it, of the first 
locational figure. P2, the location of the second stage, is the 
ninimum point of the second figure. Thus the problem of the 
Vhere" of the locations of stages of production appears to be 
3ne which falls within the realm of our analysis. It involves de- 
ermining the locations of the corner-points of new locational 
igures. These corner points are the locations of the various 
;tages of production. If we succeed in finding these comer- 
joints, our problem is solved, since these corner-points are the 
ocations of split processes of production. The mathematical 

^ Cf . supra, p. 53. — Editor. 


problem involved is solved in Appendix I, §§8-ii/^ We shall 
make use of that solution at this point. But let us first see whether 
167 we can learn from the foregoing when this split will occur. 

To attack this problem we must alter our question. The 
problem is not, when does such a split occur? but when does it 
not occur? When does production remain at a single location? 
If we look at our figures again, we shall see at once that the oc- 
currence of a single location is a particular case among the many 
possible locations of the separable stages of the process of pro- 
duction. This case is reaHzed when in the locational figure of the 
first stage the place of production coincides with the place of 
consumption; and when in the locational figure of the second 
stage the place of production coincides with the place of pro- 
duction (the deposit) of the unfinished product made in the first 
stage. If such coincidence occurs, the two locations coincide. In 
all other cases they lie apart. The problem as to when a split of 
the location will occur resolves itself into the following ques- 
tion : Under what particular condition does this coincidence of 
the sites of the separate stages of production occur? We may 
consider this question first with reference to an enterprise which 
can be split into two stages only. 

One is inclined at first blush to suggest that this coinci- 
dence can occur only in case the site of the first stage of produc- 
tion is located (because of the proportions of its weights) at the 
place of consumption, and only if, furthermore, the place of pro- 
duction of the second stage is (also due to the proportion of its 
weights) situated at the deposit of the unfinished product of 
the first stage. If this were true, the non-occurrence of a split 
would be a very rare exception (assuming that the split were at 
all possible on technical grounds) ; and practically all productive 
processes having several technical stages would have different 
locations for these stages. But not quite so many conditions 
need to be fulfilled. It is sufficient either that the production of 

^ Cf. injra, p. 234. — Editor. 


''■' the first stage is located at the place of consumption or that the 
production of the second stage is located at the deposit of the un- 
finished product. For if, upon the one hand, the production of 

■ the first stage is located at the place of consumption, then it will 

■ follow any location of the second stage which is determined by 
the proportions of weight within the second locational figure. 
It will, for example, go to the place of consumption of the sec- 

: ond stage, or to one of the material deposits or to any interme- 
diate position. The fact that it will thus follow of course makes 168 
the two locations coincident. And if, upon the other hand, the 
'i .location of the second stage is situated at the deposit of the un- 
5 finished product, the location of the second stage will follow the 
-location of the unfinished product anywhere. It will, for exam- 
ple, go to the original material deposits or to any intermediate 
position. In this case also the two locations are of course coinci- 

It is accordingly only necessary that the conditions (weight 
proportions) either in the first or in the second stage be such 
that the location is bound to follow the location of the other 
stage, and the split will not take place. The following considera- 
tion will indicate, however, how frequently this split will take 
place, provided it is technically feasible. In order for the pro- 
duction of the second stage to run after the location of the first, 
it is necessary for the unfinished product to enter into the sec- 
ond stage with a locational weight which is at least equal to the 
'■■ sum of the weight of the future product and of the weights of the 
^' added materials — all this in accordance with our previous rules. 
• Jhis means that the product will have to lose considerable weight 
^ jduring the second stage. But the second and later stages of indus- 
^ trial productive processes are usually concerned with the working 
up of pure materials, with little ehmination of waste materials 
(Materialrückstände) . These stages will therefore very seldom 
'tave such a location unless they are oriented toward coal de- 
posits. So much for that. On the other hand, the production of 



the first stage must lie at the place of consumption if it is to 
follow the production of the second stage. This means that there 
must be no loss of material during the first stage, or at least only 
as much as will be compensated by the addition of ubiquities 
This also will be very rare, since the first stage of industrial pro- 
duction is commonly concerned with bringing into existence the» 
pure material, a process which calls for the elimination of the 
waste materials. We conclude, then, in either case that the con- 
ditions leading to the coinciding of the two locations will not be 
frequent. We may say, even on the basis of this prehminary 
169 analysis: Single location of production will be the exception and 
a split of production into several locations will be the rule for 
productive processes which can technically be split. 


Our next question is: Where will the locations of the pro- 
ductive stages be when production is split? Our answer will 
make it possible further to elaborate upon the question as to 
when such splitting will occur. 

The locations of the stages it will be remembered, can be 
fixed as the corner points of the new locational figures in which 
the spHt production is carried on. We know the corresponding 
figures which have to be constructed within these locational figi 
ures according to the general locational rules. This is the key 
by which the unknown corners are discovered, as is shown in 
Appendix I, § 11.^ These unknown corners are the locations oi 
the stages of production. I refer to the result found in the Ap^ 
pendix, and I shall here apply it only to a few important cases 

*The reader will find quite tiring the reasoning employed in this and thf 
following parts of this section. It is really not intended for those who wish tc 
get the general trend of the main argument; they may omit it. But scientific 
precision requires that this analysis be undertaken ; for it is necessary to show tc 
what extent the mathematical solutions based upon our theory cover the mani- 
fold phenomena and problems of reahty. 

° Cf. p. 236, infra. — Editor. 



Let us suppose that the productive process spHts into stages 
-two at first, each of which combines two materials. The lo- 
^ cational figures for these stages would obviously be triangles. 
Since we know the weight triangles of "the two locational figures 
pi with one unknown corner," we know the circles upon which the 
I two unknown corners, the two locations, will lie. (They are the 
i two circles over M1M2 and M^C of the following figure.) We 
ft know, further, that the two locations will lie upon one straight 

Fig. 34 

Fig. 35 

line (cf. Appendix I, §§ 9 and 11) which connects two easily con- 
structed points of the two circles (at the points O and Oi of Fig- 
ure 34). The points where this line intersects with the circles 
are the locations of the split production (P and Pi of the adjoin- 
ing figure). It will be seen at once that this simple rule is gen- 
erally applicable. 

Let us now assume a productive process based upon two ma- 
terials so that the entire process will be carried through within 
one locational figure, and let us assume that it is possible to 
split the process so that the first stage of production combines 
the two materials, while the second stage uses one of the ma- 





terials (for example, coal) again in connection with the unfin- 
ished product, thus completing the product. The diagram which 
will give us the location of the two stages is simple enough (cf. 
foregoing Figure 35). The circle over the material deposits with 
the angle of the first weight triangle as its peripheral angle will be 
the general focus of the first location; while the circle with the 
analogous angle of the second weight triangle over the second 
material deposit and the place of consumption will be the general 
locus of the second location. The points and Oi situated upon 
the circles have to be determined next.^ The two points at which 1 

Fig. 36 

the straight line connecting them intersects the circles are the- 
two locations, Pi and P2. j 

Let us next assume a productive process based upon five ma- 
terials, it being a process which might technically be split into 
three stages. The first stage combines the first two materials; 
the second stage combines the product of the first with two more 
materials; and finally the third stage combines the product of 
the second stage with the fifth and last material into the final 
171 product. 

The diagram showing how the locations of these stages may 
be determined is given in Figure 36. 

In principle the diagram of the case when the production is 
split into parallel instead of successive stages is quite similar. 
Let us take for example car manufacturing. Here the metal 

® Cf. Appendix, p. 237, infra. — Editor. 



parts are worked up into unfinished products in steel foundries 
and metal works; other parts are worked up in wood manufac- 
turing processes; and still others are worked up into half-fin- 
ished products in sundry other establishments and are then 
united in the final process. The diagram of the productive proc- 
ess and of the locations of its stages appears in Figure 37. In 
short, we have found a general solution. There is just one sig- 
nificant limitation: our solution holds good only for stages of 
production which combine two materials only. Such stages have 

Fig. 37 

triangles for their locational figures. This limitation is regret- 
table in principle, but it is not as important as it might seem. 
For it will seldom occur that stages of production which involve 
:omplicated processes of combination will follow each other. And 172 
Duly where several such complicated stages of production follow 
Dne another will there be failure to determine their location by 
j:he use of the expedients we have developed thus far. In all 
Dther cases we shall always be able to construct the circles upon 
which the locations of the simpler stages of production lie (cf. 
:he adjoining Figure 38 in which M4C shows this circle for such 
m adjoining simple stage of production. This makes it possible 
:o find the line (Px—P\) upon which the location of the more 



complicated preceding stage of production will lie. We can find 
this line by using the frame of Varignon^ for the purpose of mov- 
ing one corner of the more complicated locational figure along 
the circle of the location of the adjoining stage in production). 
Through this method we have a fairly far-reaching general way 
of determining both locations. A special construction for partic- 
ular cases can of course be made with the expedients of higher 
mathematics, even if the complications are much greater. But 
we shall limit ourselves to the finding of general rules. 

Another aspect of the foregoing conclusions is of interest 
here. The simple diagram by which we can generally determines 

Fig. 38 

Fig. 39 

the locations of split production also affords us a more precis« 
answer for the question as to wheji this split will occur. Thai 
mathematical analysis of the Appendix (cf. Appendix I, § 11) 
shows that the spHt will not occur, if the circles determining thö 
locations of the stages intersect and if at the same time the de- 
termining straight line goes through that segment. 

But this is not theoretically significant, applying as it doesi 
173 only to certain geographical situations; rather, it is the conse- 
quence of an accidental proximity of the material deposits of 
the different stages. Obviously, no split will take place when thai 
intersecting point of the determining straight line is situated in 
^ Cf. Appendix, p. 229. — Editor. ; 


the common segment ; for the intersecting points go beyond each 
other (cf. the foregoing Figure 39). The elements of two stages 
of production remain next to each other after having met. A 
common location within the segment is the result. 


It is quite interesting that the construction we discussed be- 
fore suffices for determining the locations even if the splitting 
of the productive process involves a change of the material 
deposits because of the employment of new deposits. Such re- 
placement of old deposits by new ones will always occur when 
the material deposits of the last stages are situated nearer the 
place of consumption, or when material deposits of the first 
stages are situated nearer the deposits of the main materials — 
nearer than is true of the deposits which would be most advan- 
tageous within the locational figure of the unsplit production. 
The adjoining Figure 40 shows what will happen in these cases. 
The deposit M'2 has been substituted in the first stage, while the 
deposit M's has been substituted in the second stage, because 
these deposits are more advantageous for the split production 
than Mo and M3, which were most advantageous for the unsplit 
production. One can see at a glance that the finding of the loca- 1 74 
tions of the separate stages of production is not complicated by 
these substitutions. We construct in accordance with our former 
rules, using the new deposits as bases. 

This is true even if a material which was formerly supplied 
for the unsplit production by one deposit is now brought into the 
production of the different stages from different deposits, inas- 
much as it enters into the production at several stages. A fre- 
quent example is coal. The splitting of production simply neces- 
sitates the substitution of these different deposits, which then 
become the basis of our constructions, as outlined before. No 
particular difficulties ensue from that. 




Let us suppose next that an industry is oriented toward labor 
in its productive process or in parts of it. What will be the effect 
if such an industry is split up and oriented at the locations of 
the stages of production? 

If that industry is already dissolved into stages of produc- 
tion by transport orientation (which is after all the basis of 


Fig. 40 

Fig. 41 

labor orientation) the location of each stage may then be re- 
garded as the location of a separate process of production. Lo- 
cation will be influenced by the labor locations of the particular 
stage according to the rules which we know already. Deviation 
will occur if the labor location lies inside the critical isodapane 
of the respective locational figure of the stage, etc. And if de- 
viation does take place, the deviation point is substituted for the 
transport location. By becoming the location of its particular 
stage this deviation point will influence the locational figures 
of the adjoining stages. The construction of the locations of the 
stages will in consequence be simplified; for a fixed and de- 



termined corner will be substituted in the locational figure of the 
stage for an unknown comer which must be found by construc- 

The labor location will consequently alter, not only the lo- 
cation of its own stage, but also the locations of the stages pre- 
ceding and following. For these are not fixed; they are in- 
fluenced mutually, each by every other. The locations of the 175 
adjoining stages will orient themselves in accordance with the 
labor location between them, as is indicated in the foregoing 
Figure 41 which illustrates a productive process having two 
stages, in which the labor deviation influences the second stage. 
Due to this deviation, some cost of transportation will be saved 
(P\P'2 is shorter than PiP'2, which otherwise would have had to 
be used). This circumstance increases the possibilities of de- 
viation somewhat beyond the scope which could be inferred from 
the critical isodapane around the locational figure of that stage. 

I do not believe it is necessary to discuss further the small 
alteration which this involves. It is more important to note that 
in this case also former material deposits may be replaced by 
others more favorably located.^ In a split production this may 
mean the elimination of locations of entire stages of production 
and their replacement by locations which are based upon entirely 
different material deposits which happen to be nearer the at- 
tracting labor locations. Under certain circumstances this may 
mean a considerable revolution in the entire set of locations of 
the stages of production — all due to the labor deviation of just 
one stage. But this replacement of material deposits does not, of 
course, create any difficulties of construction. Theoretically its 
effect is of course exactly the same as that of replacing material 
deposits within an unsplit productive process: the attracting 
force of the labor locations will be strengthened in exact propor- 
:ion to the savings of costs of transportation which result from 
5uch replacements. 

* Cf. supra, p. 113 f. — Editor. 


We ought to mention, finally, that labor deviation itself 
may cause productive processes to split by causing the deviation 
of some location which had previously followed the location of 
176 the adjoining stage. This may be an effect of labor deviation 
which is superficially quite striking, but it does not contain any 
theoretical problem. 


On the basis of what has been said we may determine what 
it will mean if we include the factors of agglomeration in our con- 
siderations. We are dealing in principle with the same problems 
which we encountered when dealing with the deviations caused 
by labor orientation. 

A separate function of agglomeration exists for every stage 
of production and it influences that stage separately. This in- 
fluence will be exerted according to the general rules of agglom- 
eration.® The creation of centers of agglomeration — as is well 
known — is subject to the creation of segments of the sets of 
isodapanes of the locational figures of the stages of production 
which have possibilities of agglomeration. 

As in the case of labor deviation, a problem is created by 
the fact that wherever agglomeration actually occurs there may 
occur also a deviation of the locations of those stages of produc- 
tion which precede and which follow the stage within which ag- 
glomeration has occurred. But what has been said in dealing! 
with this problem in the case of labor deviation holds true also 
for the case of agglomerative deviation, mutatis mutandis. How- 
ever, this problem will be of much smaller significance than the 
one created by the replacement of those material deposits which 1 
are more unfavorably situated than hitherto unused material de- 
posits lying much nearer the new location created by agglomera- 
tion. This is due to the fact that the strengthening of the attract- 
ing force of the deviation points is much more important. 

* Cf . infra, p. 246.— Editor. 


The most important problem which remains over and above 
those questions which we encountered in the case of labor de- 
viation consists in the fact that the 'Vhere" of the point of 
agglomeration will be altered when the locational figures upon 
which this point of agglomeration is based are altered. But we 
have seen before^° that the center of agglomeration shifts also 
when the productive process is not split. It will be remembered 
that this is due to the elimination of bad material deposits. What 
has been said there holds true here: the center of agglomeration 
remains determined by the location of the places of consumption 
and of the most advantageous material deposits, and does not 
shift very much. Consequently no further discussion of this 177 
problem is needed. 

This brings us to the end of our theoretical analysis of the 
nature of orientation as related to the possible stages of a given 
productive process. Following our usual procedure, our next 
question is: upon what conditions does this nature of orientation 
within the productive process depend, and how will the known 
changes of reality affect it? 



The fact that the locations of an industry are split is the 
upshot of its technical nature. The splitting seems therefore to 
depend solely upon the general characteristics of that industry 
and to be entirely independent of environmental conditions such 
as the level of transportation costs and the density of population. 
Indeed, it is determined by the nature of the productive process; 
and any changes in that nature will also change the nature of 
the split. Speaking more precisely, the technical nature of the 
productive process of an industry and the manner in which it is 
handled will determine whether that productive process has 
technically independent parts and what materials are available 

^° Cf . p. 141, supra. — Editor. 


for each of these parts. It will further determine how the inde- 
pendence of the parts and the availability of materials are af- 
fected by the general economic development. The several loca- 
tional figures are created and altered by these facts. 

We may say in general terms that the splitting of an industry 
is facilitated when more materials are used and when these addi- 
tional materials are used in several independent stages of pro- 
duction. No necessity to split on the basis of rates of transporta- 
tion will exist for an industry which has a whole series of inde- 
pendent stages of production, of which however only the first 
stage involves combining several materials, while all the later 
stages involve only the additional application of labor. The pic- 
ture in this case will show the location of the first stage near 
the materials, while the location of all the remaining stages 
will be somewhere along the way between the location of the first 
stage and the place of final consumption. As a matter of fact, 
these remaining locations will almost always be situated at the 
1 78 place of consumption, due to advantages of the market (Absatz). 
In spite of the great number of possible independent stages of 
production, the productive process will be split into only two 
stages, which we may call the stage of materials and the stage of 
consumption. We find this as the typical picture in all those 
older and simpler industries which are carried on without the 
use of coal in the higher stages. But if materials enter into one 
or more of the later stages of production, independent locational 
figures and fixed independent locations will come into existence. 
It should be noted, however, that only the entrance of weight ma- 
terials, such as coal and coarse materials, will really prolong the 
series of locations. For the entrance of a pure material or of an 
ubiquity has the effect of pushing the production toward the 
place of consumption, and consequently does not alter the orig- 
inal picture. The use of coal in the higher stages of production is 
of necessity the main factor through which the modern develop- 
ment stimulates the sphtting of production — if it does so at all. 


But it would be a mistake to say that the tendency of a given 
industry to spHt increases in proportion to the loss of weight of 
raw materials within the higher or later stages of its production. 
For even the slightest loss of weight of an entering material 
creates the basis for an independent stage of production with a 
separate location, as far as cost of transportation is involved. 
The magnitude of this loss of weight does not in principle affect 
this situation in the least. What it does determine is the extent to 
which the location of that stage of production will be attracted 
by the deposit of the material involved. If the material entering 
the higher stages of production is coal, this attraction may be so 
strong as to reunite the separate stages at the coal deposit. 

These few sentences concerning the extent to which the 
splitting of production depends upon the extent to which ma- 
terials enter into the productive process do not exhaust the 
discussion of the conditions surrounding this splitting process. 
This spHtting will be determined by the nature of the productive 
process only to the extent that transportation costs enter. But 
we have seen that splits may also be caused by deviation due to 
labor or to agglomeration.^^ To the extent to which these devia- 1 79 
tions are possible and occurring, splits are dependent upon the 
conditions to which these two kinds of orientation are subject. 
Splitting of these parts of the productive process which have not 
formerly been separated is dependent particularly upon costs of 
transportation and density of population, since these two factors 
as environmental conditions codetermine labor orientation and 
agglomerative orientation. For example, the manufacture of 
linen clothes (Wäsche) , which was formerly deviated to certain 
jlarge labor locations, experiences at the present time a split 
which is moving the intermediate stage of embroidering such 
cloth (for the German manufacture) as far as Madeira.^- It is 
obvious that the split which has occurred in this instance is due 

" Cf . supra, pp. 184 f., 186 f. 
"Written in 1909. — Editor. 


partly to the lowering of costs of transportation, a decisive fac- 
tor. We must say a few words regarding these general tenden- 


We have said before that the technical nature of the pro- 
ductive process and its execution will fundamentally determine 
whether the various groups of industries are organized into 
stages of production, and if so, in what manner. Nothing could 
be more erroneous than to assume that the technical differentia- 
tion of the medieval trades, from which we shall start in our 
analysis of actual development, was inconsiderable. There ex- 
isted that structure of technical stages of production which re- 
sulted as a matter of course from the traditional tools which have 
been the common property of Euro- Asiatic civihzations {vor- 
derasiatisch-europäischer Kultur kr eis). These tools split the 
productive process into about as many technically independent 
parts as it can conceivably contain. For these tools became sc 
specialized that they made it impossible to control more than a 
very small part of the productive process, and they consequentl> 
tore it to pieces technically. The productive process througl: 
which the metals, wood, leather, and the fibers, as well as mosi 
food materials, had to pass was always long and had many inde- 
pendent stages. It is true, however, that two things are typica 
of the medieval economic system. First, the economic organi- 
zation which was superimposed on this technically split produc- 
1 80 tion was not split to any considerable extent. The number oi 
successive stages of production which achieved economically 
independent organization remained small.^^ There were seldorr 
more than two or three. Second, even those stages of productior 
which had become economically independent generally remained 
together at the place of consumption. No local splits into loca- 
tions of the stages of production followed the inconsiderable 

'^ Cf . regarding this point the well-known article of Bücher, "Gewerbe," m 
the Handwörterbuch der Staatswissenschaften, Vol. III. 


3conomic splits of production. It is well known that the preven- 
;ion of too numerous successive stages of production (as well as 
;heir retention at the market of the town) was a necessary part 
)f the economic policies of medieval towns. 

But what made possible these policies of grouping all the 
;echnically independent parts of production around the market 
)f the town? Obviously the fact that the technical potentialities 
:or splitting production did not yet jorce production to split geo- 
graphically. All these individual and separate parts of the pro- 
iuctive processes were largely oriented toward consumption, 
ust as we found the inseparable units of medieval crafts oriented 
oward consumption. 

To the extent to which they were not oriented toward con- 
mmption, the policies adopted for the purpose of concentrating 
ndustries within the town limits jailed. Indeed, we can com- 
Dletely understand the development of the larger part of medie- 
/al rural trades (Landgewerbe) only if we conceive of these 
:rades as ''stages of production." The trade policies of the towns 
iailed with regard to these rural trades because these policies 
:ould not overcome the locational rules according to which these 
stages were oriented toward their materials and not toward con- 
sumption. Consequently the concentrating policies of the towns 
lever attempt to inclose within the town walls the foundries; 
-hese have always been oriented toward the material deposits. 
Similarly, the towns did not attempt to draw to themselves the 
growing glassworks ; these were oriented toward the fuel mate- 
*ials. And when later (since the fourteenth century) water power 
s increasingly introduced into production and thereby increases 
:he materialization^* of initial and intermediate stages of produc- 
:ion, then these stages of production — the iron works, the copper 

"We mean by "materialization" the extent of the use of localized mate- 
•ials which strengthen the components of the materials in our locational figures. 
The change from ubiquitous to localized materials means also "materiahzation." 
^n view of this circumstance the Middle Ages had little "materiaUzed" industrial 
production on account of the extensive use of ubiquitous materials like wood. 


works, the rolling mills, and the paper mills — follow those other 
stages of production which have already been taken outside the 
towns, and they do so in spite of the concentrating poHcies of the 
i8i towns. 

It is simply the slight materialization of medieval production 
which causes the inconsiderable locational differentiation of the 
stages of production. 

It is interesting to analyze how further development leads 
to further splitting of the productive process. From our point 
of view the large textile industries organized under the putting- 
out system in the fifteenth and sixteenth centuries represent mi- 
grations of industry away from the place of consumption, their 
large-scale production supplementing or even destroying the old 
handicrafts' production. Spinning and weaving are separated 
from tailoring, which remains oriented toward consumption, 
while the former migrate to locations of lowest costs of labor. 
Obviously, from the standpoint of our theory changed environ- 
mental conditions, and not technical conditions, eliminate the 
old locational unit of the handicraft production. Those parts of 
the productive processes which become organized according to 
the putting-out system migrate to locations which have become 
more attractive because of the general improvement in transpor- 
tation together with the increasing density of population — the 
latter producing local labor surplus with ensuing possibilities for 
decreasing labor costs. 

The third great period of revolution, from the second half 
of the eighteenth century until the end of the nineteenth century, 
increases further the dispersion of the locations of the stages of 
production. This is the time when the old mercantilist industries 
operated under the putting-out system and the handicrafts them- 
selves were gradually mechanized to such an enormous extent. 
The zigzag course of production increases when mechanized 
182 spinning is torn from mechanized weaving; when the mechan- 
ized wood-planing and refining factory pushes itself in between 


the sawmill and the manufacture of various finished products; 
when the mechanical manufacture of legs appears between tan- 
nery and shoe and boot manufactures; when the manufacture 
of pulp comes into being as a separate stage of paper manufac- 
ture; when the mechanization of the manufacture of metals 
quite generally puts the factory of half-finished products (of 
the parts of locks, of watches, of automobiles, etc.) between the 
production of the raw materials and that of the finished prod- 
ucts; in short, when everywhere the mechanization of produc- 
tion creates new stages of production which have independent 

There can be no doubt that the mechanization and capitali- 
zation of production has done just that during the time of the 
great industrial revolution of the nineteenth century, thereby 
creating the impression that the productive processes were in- 
creasingly split by division of labor and oriented independently. 
It is hardly doubtful, either, that this process has served as the 
basis for the superficial doctrine of the "international division of 
labor," which is so closely connected with the doctrine of free 
trade. It will be remembered that by this doctrine we were made 
to believe that the parts of the productive processes which were 
given an independent existence by the increasing division of la- 
bor would quite freely move to their optimal locations, and that 
like parts would concentrate at these places, as if no transporta- 
tion costs were involved which would bind them locationally and 
which should therefore first be consulted regarding the locational 
distribution of these parts of the productive processes. Econo- 
mists observed how the productive processes were differentiated 
by the division of labor; they made no distinction between spe- 
cialization and differentiation into stages of production; they 
observed the independent local orientation of the stages; and 
since the idea of the division of labor had in general become the 
great pillow on which all economists went to sleep, we rested (as 
far as the theory of location was concerned) upon the idea of 


the geographical or international division of labor, a beautiful 
idea, perhaps, but rather devoid of real meaning. 

At present every glance into life makes us feel that the entire 
concept of a continual separation of new parts of the productive 
process — a concept based upon the law of the division of labor- 
is really explaining a transitory stage which is followed by g 

183 quite different and contrary development. We are today face tc 
face with the fact that the capitalization and mechanization ol 
the industrial processes have entered upon the contrary develops 
ment of concentration. If mechanization has in a certain sensi 
differentiated the productive process into its smallest parts ir 
order to subject these parts to its force and to give them theii 
appropriate form, that same mechanization is now gathering 
these mechanically well-organized parts into units. Mechaniza 
tion thus introduces through enormous concentrations a new ane 
quite as gigantic a revolution in industrial locations. Thesi i 
processes of concentration are first of all concentrations of capjc 
ital. They need not affect the technical and organizational in 
dependence of the combined parts of production; they couli 
let the former structure of the stages of production and thai 
locations remain intact. But there exist as a matter of fact man} 
connecting links between the tendencies of capital to concen 
träte and the tendencies of technique to organize — links th» 
discussion of which would lead us much too far afield at thi; 
time. But it can be said at once that the concentration of cap 
ital is creating for the concentration of organization and techni 
cal process new frameworks which will gather together produc 
tive processes which had previously been independent. Every 
one knows of the development in the iron industry; the onc( 
independent processes of mining the ore, producing and rolling 
the steel, have been gathered into one undivided process. Then 
are many parallel developments, which are perhaps less striking 

184 but not less effective. The manufacturer of worsteds who ac 
quires a spinning mill and attempts to combine it with his weav 


ing factory, the hardware manufacturer who combines all the 
different parts of production as they had grown up under the 
putting-out system; the gun-factory which includes all stages 
of production from the raw material to the finished product — 
all these are specific instances of a general development. Every- 
where the accumulations of capital stand behind these technical 
and organizational combinations as their larger framework. The 
structure of the stages of production is simplified and the split- 
up parts group themselves together again. New 'Vocational 
units" are created which sometimes include whole series of in- 
dustries. These new units must orient themselves anew accord- 
ing to their "locational weight," "labor coefficient," and "coeffi- 
cient of manufacture" resulting from the combinations. The 
necessity of an entirely new orientation may remain hidden dur- 
ing the beginnings of the development; certain strong plants 
may simply attract other stages of production and thus become 
centers of crystallization. The foundry may attract the rail- 
roHing mill or the forge works; the iron forge may attract as 
large a foundry or as large a hardware factory as seems suitable. 
But even this beginning may mean locational alterations of a 
very noticeable kind; it may cause the total or partial stagna- 
tion of industrial districts which are losing the parts of the pro- 
ductive process in which they had specialized. 

But this is not the end of the story. In the long run the move- 
ment will not end with such attractions of parts or stages of 
production to the stronger points of crystallization. That is to 
say, in the long run the movement will continue until it per- 
meates the entire industry. In the long run, then, there must 
come about a fundamentally new orientation of the new large 
units of production which have been created by these combina- 
tions. This new orientation may come about slowly, because of 18; 
the enormous fixed capital which is involved in a dislocation of 
these industrial giants and which give great weight to their lo- 
cation as it developed historically. But this new orientation must 


sometime take place if location is at all controlled by economic 
laws, and it will push the new units to the locations which are 
determined by their locational weight, their labor coefficient, 
and their form coefficient. This will complete the locational revo- 
lution which was started by the recent development toward con- 
centration. During the entire nineteenth century we were under 
the influence of a revolution in locations, a revolution which, 
starting with the unity and simplicity of handicraft organization, 
eventuated in the extremely chaotic orientation of independently 
organized large-scale industries of the old style. Today we are 
at the beginning of a new revolution which may lead us to a 
new and much more simple orientation, to units of locations of 
large-scale industries organized in combinations. 



We have proceeded thus far on the assumption that the vari- 
ous processes of industrial production are independent of each 
other without any relationship to one another. This is not the 
case. They in fact interact upon one another in various ways. It 
remains to discuss this interaction. It may be of three kinds: 

First, the production of quite different articles may be com 
bined in one plant {Betrieb). This is, from our viewpoint, a lo 
cal coupling of independent industrial processes. 

Second, the locally separate production of various articlesfk 
may be based upon the same set of materials and unfinished 
products. Here we have a connection through materials of the 
1 86 preliminary stages of several different industrial processes. 

Third, the product of one industry may enter another indus- 
try without being, as in the previous case, material or unfinished 
product, but rather "means of production" or "auxiliary prod- 
uct" (for example, wrapping material). This may be described 
as market connection of one industry with one or several others. 



If products of different productive processes — and since 
each product has theoretically its own process, we may simply 
say, if different products — are produced in the same plant^^ 
this may be due to either technical or economic reasons. It is 
possible that for technical reasons several products of different 
kinds must be produced at the same time, as for example in 
certain chemical industries. But this technical necessity may be 
absent. The factory which produces cables, accumulators, and 
other electrical apparatus, the garment factory which manufac- 
tures overcoats, capes, shawls, blouses, etc. at the same time, 
does so for economic, and not for technical reasons. This dif- 
ference is rather significant in general as well as for location. 
I The coupling of productive processes which results from a 
«connection of technical factors makes one location for several 
kinds of product imperative. It may be regarded as the bifur- 
cation of a unitary process of production at the place of produc- 
tion. Not one, but several, places of consumption influence the 
location; and from our discussion of agglomerated production 
we know the influence and significance of several places of con- 
sumption. We know that the existence of several places of con- 
sumption does not seriously complicate the determining of the 
location. True, we must take the components of several places 187 
of consumption into account when considering the orientation 
of this type of production. The locational figure which results 
has several components of consumption, their number depend- 
ing upon the number of kinds of product. These components 
must be weighted with the weights corresponding to the kinds 
of products. That is all. The locational figure of an isolated unit 
of production will look somewhat like Figure 42 (next page) for 
plants which combine two kinds of production. The location will 
then be determined according to the general rules. 

^°By plant (Betrieb) we do not mean enterprise, since an enterprise does 
not need to be confined to a local unit of manufacturing. 


One might think that the same situation would arise when 
the coupling was technically not necessary. Without doubt the 
locational figure which is finally created will be quite similar. 
But it will be created in an entirely different way, and has 
therefore, locationally speaking, quite another meaning. This 
locational figure of the coupled processes will always involve a 
deviation by which those processes will be moved away from the 
location which they occupied when they were isolated, except in 
the unusual instance in which the coupled processes have the 
place of consumption and the material deposit in common. Ob- 
viously the coupled productive processes would have had dif- 
ferent locational figures and different minimum points if their 

Fig. 42 

material deposits and places of consumption were different. If 
their production is actually coupled, a deviation from those 
minimum points must have taken place. This kind of coupling, 
then, will follow the rules of deviation which we have found for 
the labor orientation and for the agglomerative orientation of 
industries, and it must be analyzed accordingly. This analysis 
may be determined by the special nature of labor deviation asi 
well as by that of agglomeration. 

It may happen that the coupling of several productive proc 
esses at the new location takes place because this location hasi 
a labor supply which renders certain savings possible for each 
of these processes. The particular skill of these laborers may, 
for example, protect these industries better against the evil ef- 
fects of business cycles or changes of fashion. This really con- 
stitutes no peculiar problem. Such labor locations are points 


toward which the several processes will deviate; such locations 
will attract these processes according to the influence which their 
index of savings has for each process. As we have seen,^^ this 
influence will be determined by the respective labor coefficients. 
The elimination of unfavorable material deposits, the increase 
of the attracting force of large locations, all this will take place 
according to the rules which we know. The only difference is 
that each place attracts several productive processes of differ- 
ent kinds, and not processes of an identical kind. We need 
therefore to analyze the way in which these processes are in- 
fluenced separately. That is simple. 

The other case seems more complicated. It may happen 
that the coupling of productive processes and the deviation 
which it entails are due to agglomerative forces. Coupling takes 
place because through such a connection of productive processes 
it is possible to eke out advantages which are unattainable by 
divided production. These advantages may be due to organiza- 
tion, to the use of machinery, to wholesale buying and selling — 
any or all of which the separate processes did not permit on ac- 
count of their small size. A unit of agglomeration made up of 
several industries will come into existence. This unit of ag- 
glomeration will be determined by a function of economy or a 
function of agglomeration^^ which is related to several industries 
instead of being related to one. There is nothing peculiarly diffi- 
cult about the question of how this function of economy agglom- 
erates the individual productive processes of the industries in- 
volved. We merely apply the rules which, as we have found, 
determine the formation of segments by the isodapanes. The 
difference — the new element — is that the isodapanes of several 
different industries are involved. 

But the application of the general formula of agglomeration 
seems to be rather difficult. This difficulty would in turn render 
difficult the understanding of the final orientation of such com- 

'® Cf. supra, p. no f.— Editor. " Cf. pp. 126, 246.— Editor. 


bined production. It seems that we shall have to apply the sev- 
eral functions of agglomeration of the several industries. But 
although this formula is a theoretical makeshift (as we have oft- 
en emphasized), a solution is not as difficult as may at first sight 
189 appear. In our formula of agglomeration we shall have to sub- 
stitute the f(M) (the function of agglomeration) of the com- 
bined productive process and its locational weight (A). If we 
ask which tendencies of agglomeration does any one of these 
products follow, the theoretical answer is twofold. If the prod- 
ucts are all produced separately, they will follow the tendencies 
which are indicated by their individual formula; if they are 
produced in combination or coupled with others, they will follow 
the tendencies which are indicated by the formula of agglomera- 
tion of the combined process.^^ But generally this complicated 
formula will not be necessary for the arbitrary combination of 
several different productive processes in the same plant (plant, 
not enterprise; cf. foregoing) will as a rule be profitable only 
provided similar kinds of labor, of machinery, or of materials 
are used for the different products. ^^ This means that arbitrary 

^^The meaning of the text is not certain here. It reads: ". . . . Wenn sie 
alle getrennt produziert werden, den und den, die sich aus der einfachen Formel 
ergeben; wenn kombiniert, mit den und den anderen produziert wird, den und 
den, die sich aus der Kombinationsiormel ergeben." It is likely, from what is 
said in this paragraph as well as in previous chapters, that this sentence refers 
to the following problem : Will a given productive process, under the influence 
of various agglomerative tendencies, enter an agglomeration which does not 
involve a coupling of it with other productive processes, or will it enter a unit 
of agglomeration which does involve such coupling? It must be supposed that 
some of the agglomerative tendencies referred to issue from a unit or units of 
agglomeration which do not involve the coupling of the several productive proc- 
esses which are being attracted; while other tendencies issue from a unit or 
units of agglomeration which do involve such couphng. The answer to this 
problem, following as it does from comparison of the two or several formulas, 
seems to be indicated in the text. — Editor. 

" The situation is of course quite different where coupling is technically 
necessary. In this case it is quite usual for the products which emerge from the 
same materials to require quite different kinds of machinery and labor. But it 
would not be worth while to combine two products which are essentially dis- 


combination can take place only if a productive process has 
the same function of agglomeration and the same material index 
no matter whether it agglomerates the productive processes of 
one, or of another, or of several of the products. We do not have 
to distinguish, roughly speaking, between the agglomerating 
processes of isolated and of coupled productions. The formula 
of agglomeration of the one is identical with that of the other. 

This consideration of the arbitrary coupling of productive 
processes yields a rather important by-result. The density of 
production, it will be remembered, must be taken into account 190 
in considering the probable extent of agglomeration of a pro- 
ductive process in reality; it must be entered into the formula 
of agglomeration. This density of production must be deter- 
mined from the amount of space required by all the productive 
processes within a given area which are similar to each other 
and may be coupled and combined into units of agglomeration. 
For this amount of space apparently determines which agglom- 
erations either of separate productive processes or of coupled 
processes will come into existence in reality. That this is true 
will hardly need further proof after all that has been said; but 
it is probably the most important result which the foregoing 
analysis yields, supplementing the general theory of location. 


Independent productive processes may be connected by the 
materials which they use, and such connection may be due either 
to technical or economic factors. Productive processes are 
technically connected if the material of one process is the by- 

similar in these particulars unless such combination were technically necessary, 
since neither a more intensive use of the machinery, nor of labor, nor wholesale 
buying of materials could be achieved — all of which means that the most impor- 
tant savings of agglomeration are absent. As a matter of fact only these two 
forms exist in reality : Technically necessary coupling of partly differing produc- 
tive processes, and arbitrary couphng of loosely related productive processes. 
Concerning by-products, cf . infra. 


product of the second main product of any one of the stages of 
another process. For example, the woolen industry is connected 
with certain lines of the leather industry through its materials, 
because leather branches off as a second main product of one of 
the initial stages of the production of wool. Similarly, the dye- 
stuff industry is connected with other industries using coke, 
because coal tar (upon which the dye-stuff industry is based) is 
a by-product of the burning of coke. Productive processes are 
economically connected by their materials, if a given raw ma- 
terial, or a given unfinished product may be used either for the 

Common Raw Material ^^^ 

Fig. 43 

one process or for the other. This case is very frequent. Our mod- 
ern industrial structure, enormously differentiated by innumera- 
ble branches functioning as independent productive processes, 
is rooted in a few raw materials which it is not very difficult to 
enumerate. In other words, large parts of this industrial struc- 
ture are connected by materials, since groups of raw materials, 
such as wood, metals, soils, leather, etc., may be used alternative- 
ly by the different parts. 

The effect of these two kinds of connection through mate- 
rials (technical connection and economic connection) is in no 
191 way the same. 

Each individual productive process connected for technical 
reasons with another productive process through a material will 
at a certain place join the other process (cf. the adjoining 
schema. Figure 43). If the materials of the different industries 
as they come into existence at the junction show a distinct order 


of rank, i.e., if one of these materials is the main material while 
the others are distinctly by-products,-*^ or even waste, the result- 
ing problem of orientation is simple. The process whose mate- 
rial is the main material is the controlling one, and the common 
initial stage will be oriented toward the location of this process. 
The resulting location is the material deposit of the other indus- 
tries which use the by-product. There remains no problem. 

But a problem does remain if all the products which are pro- 
duced at the junction point are of importance from a locational 
point of view (this being either due to their weight or to their 
value, cf. the last footnote). In this event this connected stage 192 
is a part of several equally important or similarly important 
processes of production; it has therefore two or more lines of. 
production continuing it. All of these lines of production influ- 
ence the location of the junction point which is their common 
initial stage of production. Consequently the location of this 
junction point is not apparent without further analysis. The so- 
lution is the same as in the reverse case, in which two or more 
different series of productive processes are united into one prod- 
uct by a process of combination. We need only imagine the fig- 
ure which was given on page 181 to be applied in reverse geo- 
graphical position in order to see how the common initial location 
(which is here substituted for the common final location there), 
and the succeeding locations of the several series of productive 
processes will influence each other. 

^ They may be by-products, because they are very inferior in weight, al- 
though equal in value. In that case they do not have any effect whatever upon 
the location of the junction point because their determinant is too weak. Thus 
wool does not appreciably influence the orientation of the co-product, leather, 
although wool is a second and valuable product of the tannery, or may be such 
at least. On the other hand, by-products may become trifling influences because 
they are greatly inferior in value, if not in weight. They would have to have an 
effect upon the location if they would not be eliminated from consideration for 
economic reasons. This is the case of bones in the slaughter-house. The location 
of the slaughter-house will not be influenced appreciably by the realization of 
the bones, because the by-product has, comparatively, too small a value. 


Much simpler is on the whole the case in which different pro- 
ductive processes are connected by materials on account of 
economic reasons. This case is also much more important be- 
cause it permeates the entire industrial structure. Theoretically 
we have to start from the idea of individual productive processes, 
as that idea has always been used so far. The transport orienta- 
tion of the individual process, in which materials are used which 
may be used alternatively in other and different processes, will 
nevertheless take place according to the simple and well-known 
rules, without regard to whether the material may be used in 
other processes. The individual productive process does not need 
to concern itself — and therefore will not concern itself — about 
whether its material will also be used in different productive 
processes, any more than it concerns itself about whether its 
material will be used in other individual processes of the same 
kind of industry. It follows that the basic transport orientation 
within the economic structure (from which we always have to 
start in our analysis) will be quite indifferent to such connec- 
tions through materials. The basic transport orientation will 
not be affected by the fact that iron is today an important raw 
material in several hundred different series of productive proc- 
esses and will be supplied to these series from the same deposits. 
193 The same is true of wood, leather, etc. The groundwork of loca- 
tions as determined by the costs of transportation — considered 
for the time being apart from its alteration due to agglomeration 
and labor — will not be affected by whether a hundred different 
kinds of productive processes will use one and the same material 
from the same material deposit, or whether they will use a hun- 
dred different raw materials which happen to come from one and 
the same deposit. The different processes become internally in 
no way dependent upon one another because they all use the 
same raw material; they merely happen to have the same geo- 
graphical starting-point, nothing more. 

The importance of the possibility of such a common geo- 



graphical starting-point becomes apparent only when we con- 
sider that agglomeration and labor orientation influence the 
transportational groundwork. But no new locational problem is 
created, at that. Just as agglomeration and labor orientation 
will create locations of common orientation for the initial stages 
of the same industry, so they will create such common orienta- 
tion for those stages of different industries which use the same 
material or half-finished product. The result is the same as in 
the first case. The individual stages of production, which be- 
long to different succeeding processes of production (i.e., be- 
long to different industries), will agglomerate according to the 
same rules and in the same way as those stages which are the 
initial stages of the same kind of production. It is of importance 
for this agglomeration that the different processes be rooted in 
the same place and therefore He near one another, but nothing of 
theoretical significance can be said about it. However, it is 
probably fortunate that the picture of the originally isolated 
orientation of the different productive processes connected in 
fact through their materials and the picture of their agglomera- 
tion according to our general rules will render lucid and simple 
the apparently very complicated problem of how the orientation 
of these different processes is interrelated within the industrial 
structure. The entire industrial structure is permeated by such 
"economic" connections through material; and it seems at first 
almost impossible to consider the orientation of an individual in- 
dustry in isolation and to define rules for it, since a great many 
other industries seem to influence its orientation. Still, such 194 
isolated consideration and analysis is seen to be possible and 
admissible now that we have seen that the "economic" interre- 
lations through materials create only secondary alterations of 
the groundwork of the transport orientation — an orientation 
which is built up upon the basis of the isolated processes of pro- 
duction and is quite independent of such economic interrela- 


tions.-^ These deviations take place according to the same rules 
that would be operative if the entire industrial organism were 
one single and uniform industry. I believe that an understanding 
of these considerations will justify the manner in which our 
entire theory is built up — using, as it does, an isolating analysis 
of the individual industries or even of the individual process of 


As stated before, the product of an industrial process may 
enter into another industrial process without being used as ma- 
terial or half-finished product; it may be a fixed means of pro- 
duction or an auxihary product. The new situation, as compared 
with the cases studied thus far, is constituted by the fact that 
the two industrial processes are no longer connected by a com- 
mon place of production. Instead, they are connected by the 
fact that the one productive process creates places oi consump- 
tion for the other; this situation exists v^here they are connected 
through some means of production. Or they are connected by 
the fact that a common market is created (where for example the 
main product and the wrapping material are brought together) ; 
this situation exists where the processes are connected through 
some auxiliary product. Neither of these situations can be called 
"a connection of production" since there takes place no trans- 
formation of materials which would create new products. No 
organic connection of the two productive processes takes place. 
The connection is based solely upon the linking of the market of 
the one with the other. 

This connection may have very important consequences in- 
fluencing the location at which the means of production or the 
auxiliary product are produced, quite apart from the fact that 
the locations of these productive processes are in any event in- 
fluenced by the places of consumption created by the main 

^ These rules have been elaborated for the deviations due to labor and ag- 
glomeration, as set forth in chaps, iv and v. — Editor. 



process. It may be, and often is, the case that the manufacture 
of the means of production, or of the auxiliary product, will be 
drawn toward the location of the main process so strongly as to 
become united with that main process. If this occurs in ac- 
cordance with our general rules of location (i.e., because the 195 
locations within the locational figure of the auxiliary process 
are situated at the place of consumption, thus following their 
material index) then this situation contains nothing theoretically 
remarkable. The locations of the production of the main indus- 
try are the locations of the auxiliary industry simply because 
the former are the places of consumption of the latter. But if the 
auxiliary process is drawn to the location of the main process 
for special reasons (for example, because the auxiliary industry 
needs, on account of the nature of its product, local contact with 
the production of the main process — which happens for example 
often in the manufacture of machinery), then a special situation 
seems to arise. But may it be emphasized at once, no real prob- 
lem appears. All we can say here is that special locational fac- 
tors — and such special factors will often interfere with the rules 
of the theory — will draw the location of the auxiliary industry 
to the place of consumption although, according to the general 
rules, it should lie elsewhere. As the place of consumption is 
definitely given by the main industry, nothing remains unde- 

It may be well to indicate here that without doubt special 
locational factors have extensive application to the production of 
such means of production and of auxiliary products. In fact, 
these special factors are the very ones which make the nature of 
these industries as auxiliary industries quite apparent even at a 
cursory glance. But it should be emphasized that whether or not 
such a connection of the places of production is caused by such 
special locational factors, the fact will not at all alter the funda- 
mental locational nature of these industries. An industry manu- 
facturing machines will remain an industry connected with the 


market or consumption place of its main industry, and this is 
true whether its locations are drawn to its places of consump- 
tion (say, the locations of the main industry) or whether it 
orients itself within its own locational figure according to the 
general rules. It would be quite wrong to narrow the definition 
of an auxiliary industry by requiring the existence of such local 
contact. Any industry which is connected with a main industry 
196 by its market is an auxihary industry. 

The only instance in which such market connection yields 
anything for our general theory occurs when the location of the 
main process is affected. This is possible; the necessity for lo- 
cal contact may cause the main process (if at a certain stage 
it needs certain kinds of machinery) to tend toward the loca- 
tions of such machinery, for there it would find opportunities 
for easy and dependable repair and such stimulus to further 
technical development as would result from local contact. In 
that case the main process may perhaps deviate to the locations 
of the manufacture of such machinery. But this type of devia- 
tion is known to us already; it belongs in the category of ag- 
glomeration. For the machine factories on their part will, for 
the purpose of local contact, try to find locations in which they 
are kept fully busy. These locations are the units of agglomera- 
tion of the main process. We have seen how this local contact 
with machine factories (cf. 129 supra) is one of the factors 
which create these units of agglomeration. 

Here, as before, it may be a bit difficult to see clearly the dy- 
namic working of these forces. The want for local contact is the 
reason why the machine industry, to stick to our example, ori- 
ents itself toward the location of the main process of production. 
The resulting tendency to come into contact can be realized, but 
it can be realized only at locations having considerable produc- 
tion of this kind. This tendency also exists in the case of the 
main process, and means a saving for it; but since such saving 
appears only in units of agglomeration to which it is linked from 


the other side, it becomes an agglomerative factor and therefore 
influences the main industry according to the rules of agglom- 
eration. The manufacture of machines goes to the places where 
the main industry agglomerates; and the main industry agglom- 
erates there partly because the manufacture of machines goes 


We have given a picture of the connecting links between the 
different industrial processes which are of importance for loca- 
tions. Apart from the technical coupling of productive processes 
and technical connection through materials, they all represent 
merely secondary alterations, if alterations at all, of the ground- 
work of industrial orientation as built upon the basis of theoret- 
ically isolated branches of industry. All these secondary altera- lo' 
tions take place according to the general and simple rules of 
location. These alterations are in fact but certain special aspects 
of the familiar deviations due to labor and to agglomeration, 
and they are subject to the well-known rules determining such 
deviation. The two technical relations connecting productive 
processes which really do interfere with the groundwork of 
transport orientation both take place according to well-known 
rules. They really are but one and the same phenomenon as con- 
sidered for different stages of production. Their interference in 
no way destroys the general theoretical basis upon which our 
analysis of orientation was built. 

Thus, this basis and the rules developed from it really em- 
brace quantitatively and qualitatively the final and entire orien- 
tation of industry. Quantitatively, because they cover industrial 
productions of every kind; qualitatively because they include all 
these productive processes in their theoretically isolated orien- 
tation as well as in their final orientation, having regard to all 
general relations which affect them. We arrive at a complete 
theoretical understanding of the final orientation if we start with 
the individual industries, if we then come to a clear understand- 


ing of the points of minimal transportation costs for each indi* 
vidual series of productive processes going from the places of 
consumption back to the material deposits, and if we finally 
analyze, according to the rules of labor deviation and agglom- 
eration, the ways in which these individual series are connected 
with each other and are woven together into that seemingly very 
complicated tissue which the modern industrial structure repre- 
sents. All this, including the connection between the productive 
processes of dissimilar products, is theoretically clear and serves 
to explain the development of the comphcated combinations 
which we so often encounter today in the actual industrial world 
198 with its manifold goods. 





The question now arises as to what extent our rules as devel- 
oped so far will determine the local distribution of all the units 
of industrial production within the definite geographical limits 
of a country. This question is by no means answered by all that 
has been said so far. It might be that the rules thus far evolved 
determine the local distribution of production in all its com- 
ponent parts as dependent upon one another and still leave open 
the possibihty of production grouping itself in very different 
ways throughout the land. 

This is in fact the case. We shall try, therefore, to reveal the 
limits of the pure theory of location by placing the manufactur- 
ing industries in the setting of the whole economic system. It is 
obvious that our previous discussion can give a definite picture 
of the orientation of industry only upon the basis of the hypoth- 
eses upon which it was built. It will be remembered that these 
conditions were fourfold, namely, ( i ) that the location and the 
size of the places of consumption are given as fixed; (2 ) that the 
location of the material deposits is given; (3) that the location 
of the labor locations is given; (4) that the labor supply at these 
latter is unlimited at constant cost.^ If these hypotheses be al- 199 
lowed, the theory as stated so far will positively determine the 
location of each particle of industrial production.^ 

^It will be observed that this involves the assumption of a (only theoretic- 
Uy possible) complete mobility of labor. The foregoing passages have been 
somewhat changed from the original in order to recall as clearly as possible 
vhat has gone before. — Editor. 

^ In the original the following methodological observation is inserted at this 
joint : "It is no flaw in the theory that the picture which is created thereby is 
lependent upon certain other factors, such as transportation rates, density of 


But these hypotheses should now be subjected to analysis. 
The location and the size of the places of consumption are from 
the viewpoint of locational theory no more given than are the 
locations and the wage level of labor. Nor is the location of the 
200 material deposits, at least of the agricultural ones, so given. 
On the contrary, these are matters which are determined to a 
certain extent, or perhaps completely, by the prevailing loca- 
tional conditions. For that reason they cannot be presupposed 
in a theory of location; rather they ought to be explained. We 
must get behind this assumption that they are given, because it 
was only justified as an aid in our analysis. An attempt to look 
behind this assumption will show whether the theory as devel- 
oped thus far suffices to explain industrial location, or whether 
it has perhaps gaps which must be filled by another approach. 

"To analyze the elements which were assumed as given' 
involves an analysis of our locational rules as they will actuall> 
operate within the living economic system as a whole. There 
appears at once before our imagination the picture of a circle ol 
forces which it seems hardly possible to break through. The lo 
cations of the places of consumption, the labor locations, and th( 
material deposits, which supposedly determine the orientatior 
of industries, are themselves resultants of this very same in 

population, locational weight of the industries, and the indices of value addec 
through manufacture and of labor costs. The introduction of these factors doe; 
not detract from the completeness of the theory ; for these factors are indeed 'giv- 
en' from the viewpoint of locational theory. They are subject to rules which an 
distinct and independent of locational theory. Transportation rates and materia 
indices are a resultant of the general technical development, while the indices ol 
labor costs and of value added through manufacture are partly a resultant of thl' 
development and partly a resultant of the general development of economic or- 
ganization and industrial technique. The density of population and of produc- 
tion also has its roots outside of the locational sphere, at any rate in the general 
form in which it figures as a determining factor in our theory so far (namely, ai 
the general ratio between the size of the population or of the amount of prod- 
ucts demanded and the area). In all these conditions we do not assume anything 
which the theory itself ought to explain." (This is slightly abbreviated.) — Editor 


dustrial orientation. For each particle of industrial production 
which moves to a certain place under the influence of locational 
factors creates a new distribution of consumption on account of 
^the labor which it employs at its new location, and this may be- 
come the basis of further locational regrouping. Such a particle 
of industrial production creates a new basis for material deposits 
which will be used (or, in the case of agricultural materials, even 
created), which in turn will be partly the basis of further re- 
orientation of industries. 


I In order to break through this circle we might say: each 
Hequilibrium of industrial location at a certain given moment is 
a modification of a previous equilibrium, and this modification 
[las been necessitated by the development of the general condi- 
tions of locational distribution. Viewed from the particular 
period, such an equilibrium would appear as a rational trans- 
formation of a historically developed system which had become 
oartly irrational and was therefore transformed. This historical 201 
system of locations of industrial production, of places of con- 
sumption, and of material deposits is the given reality; and by 
operating upon this basis, our rules will determine the locations 
according to the development of the general conditions, such as 

[ates of transportation, material indices, etc. 
Without doubt such an assumption of a basis as given in 
ime rather than in thought will be a valuable aid for the investi- 
'gation of industrial locations. In no other way will it be pos- 
sible, for example, to analyze the locational developments within 
:he German economic system since 1861. But it is obvious that 
:his historical basis is something entirely different from what 
Ne are looking for at present. This historical basis is the ma- 
:erial, so to speak, which is transformed; whereas we are looking 
'or a basis or theory of this transformation itself. We want to 
ind the general basis upon which the new system orients itself. 
We have construed such a basis thus far by assuming as given: 


places of consumption, material deposits, and labor location. 
Since nothing is to be assumed as given for the new system 
which we wish to analyze, we must try to analyze further the 
whole economic system itself. 


What is the most general force which connects the different 
parts of an isolated economic system from the point of view of 
location? We shall recognize it if we ask ourselves what force 
determining location would develop if some people were to oc- 
cupy a new and empty country for the purpose of building up 
such an isolated economic system. We assume, of course, that its 
local grouping will be determined entirely by economic con- 
202 siderations.^ 

Under such circumstances ^'layers" or ''strata" of locational 
distribution would develop. These strata would be interrelated, 
i.e., they would affect each other. It is obvious that there must 
be a first stratum of local distribution of industries which will 
become the basis and the starting-point of all further develop- 
ment as soon as the (supposedly limited) area of settlement is 
chosen. This first stratum must be the agricultural stratum, 
whatever may be the conditions in any other respect, and wheth- 
er or not cities are at once founded ; for under all circumstances 
the settlement of agricultural lands must take place to an extent 
sufficient to produce the necessary agricultural products for the 
whole population. In order to achieve this purpose the requisite 
part of the population must distribute itself over as large an areai 
suitable for agriculture as is necessary for the production of this 
necessary amount of agricultural products, given the prevailingi 

' These problems have recently been discussed from a new and interesting i 
viewpoint by Hans Ritschl, "Reine und Historische Dynamik des Standorts der 
Erzeugungszweige," Schmoller's Jahrbuch (1927), pp. 813 ff. ; cf. also Introduc- 
tion above, p. xxxii. — Editor. 


conditions of the natural environment, technique, and organi- 
zation.* 203 

This first stratum of local distribution — this settled area 
with its population, the agricultural stratum — represents the 
geographical foundation for all other strata. It represents such 
a foundation first of all for that part of industrial production 
(the primary industrial stratum, it may be called) which works 
directly for it. The places of consumption for all stages of this 
primary industrial stratum are given by the local distribution 
within the agricultural stratum. If we recall our rules it will be 
evident that this second stratum of local distribution (this pri- 
mary industrial stratum) is oriented under the influence of ag- 
riculture. Agriculture fixes the places of consumption, the ma- 
terial deposits, and the locational figures. 

But there are a number of other large groups for which a 
place will have to be found in our structure of locational distri- 
bution: (i) The industrial population which is engaged in sup- 
plying the wants of the primary industrial stratum for industrial 

* In the original the following observations are inserted here : "It does not 
concern us for the present that this area may be more or less densely populated 
and depending upon this degree of density may be somewhat larger or smaller 
as the further strata of locational distribution (concentration in cities, etc.) de- 
velop. Both these developments will take place in accordance with the well- 
known law of Thiinen about the relation of the different degrees of intensity of 
agricultural production and the distance of that production from the place of 
consumption [Cf. Johann Heinrich von Thünen, Der Isolierte Staat, and above, 
pp. xix ff. — Ed.] It is certain that some relation exists between the number of 
people who want to live in an isolated economic system and the area which is 
needed for agricultural production (a certain natural environment, standard of 
living, as well as a development of technique and organization). This ratio can 
oscillate only between the Hmits just discussed. It is of course possible, and occurs 
frequently, that this area of agricultural production is chosen partly with a view 
to advantages to other industrial production such as that of raw materials. But 
that does not alter the fact that the size of this area is the foundation of the whole 
structure of strata of locational distribution. And this size is necessitated by 
the wants of the whole system for agricultural products." This is slightly abbre- 
viated, and a footnote of the original text is worked into it. — Editor. 


goods; (2) the population engaged in circulating the goods pro- 
duced through trade and transportation; (3) that group of the 
population which only consumes, like officials, free professions, 
persons living on their own private means; and finally (4) the 
industrial population which supplies the wants of these last two 

The group of industrial population supplying the primary 
industrial stratum is determined by it just as this latter stratum 
204 is determined by the agricultural stratum. The primary indus- 
try creates the geographical layout of the sphere of consump- 
tion and thus creates the framework of the locational founda- 
tion. It should be noted, however, that in a strict sense this 
industrial stratum which is oriented under the influence of the 
primary industrial stratum is not a single whole, but is itself di- 
vided into numerous substrata. If we assume that the division of 
labor is highly developed, we shall find first a substratum which 
is directly engaged in supplying the wants of the primary indus- 
try; next we shall find a substratum which is engaged in supply- 
ing the wants of the foregoing substratum; another one which 
works for this one; and so on. There will be a number of sub- 
strata or layers (superimposed on each other and decreasing in 
size) of which each gets its sphere of consumption and therefore 
its general locational foundation from the previous one. If we 
suppose, for example, that 50 per cent of a people are agricul- 
turists while the other 50 per cent are engaged in industrial 
pursuits (and the country has only the strata which we have dis- 
cussed thus far), then obviously 25 per cent of the population 
will suffice for supplying the industrial products wanted by the 
agriculturists, since 50 per cent suffice to do it for the whole peo- 

^ Offhand it might be suggested that we treat the domestic servants as a 
special stratum. But from the viewpoint of locational analysis these people are a 
part of the consuming stratum to which they belong; they do not necessitate 
separate treatment. 


ple.^ In other words, the primary industrial stratum oriented 
under the influence of agriculture will contain 50 per cent of the 
industrial population. For these 50 per cent a further 25 per 
cent of the industrial population must suffice to supply its de- 
mand for industrial products. These 2 5 per cent are the first sub- 
stratum of the secondary industrial stratum oriented under the 
influence of the primary industrial stratum. In turn, another 12.5 
per cent must suffice for supplying this first substratum. These 
12.5 per cent would then be the second substratum, and for sup- 
plying their wants 6.25 per cent must suffice — ^which would be 
the third substratum. This example illustrates how the indus- 
trial population is intertangled in substrata or layers of decreas- 
ing size and how each substratum is the locational foundation of 
the succeeding one. But we need not concern ourselves further 
with these interrelations. The whole structure has its founda- 
tion in the local distribution of the primary industrial stratum 
oriented under the influence of agriculture. We shall treat these 
substrata collectively as the third great stratum, the "secondary 
industrial stratum" which is oriented under the influence of the 
primary industrial stratum. 

If we now think of this third stratum together with the first 
two as one whole, we have before us the economic system. The 
locational distribution of the largest part of the remainder sim- 
ply leans upon it. The role of such groups as have not yet been 205 
discussed is simply one of a proportional strengthening of the 
different parts of this system. 

This strengthening of the existing structure is illustrated by 
all those parts of the population which attend to the actual ship- 
ping of material goods from one location to another (the retail 
traders and the transportation agencies),^ and thus handle the 

® This seems to presuppose an equal amount of consumption per individual 
throughout, that is, an equal standard of living as far as industrial products are 
concerned. Otherwise the foregoing statement would not hold good. — Editor. 

'^ Cf . Introduction above, p. 4. 


process of circulation. Similarly, the large body of officials with 
local functions represent merely a strengthening of the existing 
locational distribution. These officials are distributed largely 
according to the general distribution of population, and are 
therefore from a locational viewpoint only exponents of it. This 
whole mass of local tradesmen and functionaries need not be 
differentiated from our previously discussed strata at all. If one 
wishes to separate them, however, one may think of them as a 
local organizing stratum, for purposes of classification. 

A really independent stratum is made up of the other parts 
of the population engaged in the circulating process and the 
groups which only consume. Of the former this stratum would 
include all those who are engaged in the general organization and 
managements of the exchange of goods, whether material or im- 
material; of the latter it would include those officials who do not 
have local, but general, organizing functions — the liberal pro- 
fessions and those persons living on their private means. All 
these persons show tendencies of stratification totally different 
from those of the local organizing stratum. They seem to be 
quite free in the choice of their locations. They appear to be ele- 
ments of the economic system very little subject to economic 
causes in their choice of their locations, as in the case of persons 
living on their private means, intellectuals, artists; or, if they 
are subject to economic causes, such causes operate upon them 
in a very complex way and are mixed with other causes (as is the 
case of officials in the central government and wholesale trad- 
206 ers). But be that as it may, what primarily interests us here is 
the fact that the locational distribution of these elements is 
something separate and independent. If they are oriented in re- 
lation to the economic system at all, they are oriented in relation 
to it as a whole and as it is created by the three or four previous- 
ly mentioned strata. Although their stratification is of varying 
types and subject to quite varying rules, they belong in one 
group in the sense that their stratification can only take place 


upon the foundation of all the other strata we have discussed 
before. We shall refer to this group under the term "central or- 
ganizing stratum." 

There remain those parts of the population which supply 
the wants of the last two strata, the organizing strata, as we have 
called them. These parts of the population will be partly indus- 
trial and partly either local organizing strata or central organ- 
izing strata. Superimposed on these there are the industrial and 
other substrata supplying the groups just mentioned, which in 
turn possess their dependent substrata, and so on. These groups 
telescoping each other ad infinitum do not need to concern us. 
For we need only separate out those substrata depending upon 
the central organizing stratum, since the substrata depending 
upon, and following, the local organizing stratum will merely 
contribute to the existing local distribution, for that, as we have 
seen, is precisely what the local organizing stratum does. But 
the stratum depending upon the central organizing stratum con- 
stitutes the fifth stratum, which we shall call the "central de- 
pendent stratum." Its substrata consist of industrial units inter- 207 
spersed with local and central organizing groups. But we may 
ignore the central organizing groups as numerically not impor- 
tant, while the local organizing elements are to be thought of 
as strengthening further the industrial units. For purposes of 
practical analysis we may treat this entire group collectively as 
one single stratum the locations of which are determined by the 
industries it contains and are dependent upon the central organ- 
izing stratum. 

We have now found: (i) the agricultural stratum, (2) the 
primary industrial stratum, (3) the secondary industrial stra- 
tum, (4) the central organizing stratum, (5), the central de- 
pendent stratum. The local organizing stratum is embraced in 
the first three as a strengthening element. These strata afford us 
a systematic understanding of the whole mechanism of stratifi- 


cation — an understanding which is sufficient for practical pur- 

The locational forces which connect the different strata play 
back and forth from the upper strata to the lower, as well as 
from the lower to the upper ones. The location of the centers 
based upon the non-agricultural strata creates the places of con- 
sumption for agricultural production; around these places of 
consumption the agricultural production groups itself in circles, 
as Thünen has shown.^ This formation of circles creates not 
only a certain geographical distribution of the kinds of agricul- 
tural production, but also a distribution of the agricultural pop- 
ulation, since the agricultural population ranges itself according 
to the intensity of production. In so doing these circles change 
to a certain extent the foundation of the whole pyramid of strata. 
This causes one of those rounds of interdependent forces which 
make the analysis of economic life such a thorny task. When we 
come to the empirical analysis we shall have to take up this prob- 
lem created by these changes of the foundation of the pyramid 
208 of strata and of their quantitative importance. All that I wish to 
show now is that these changes do not destroy the theoretical jus- 
tification of the locational structure which we have erected. It 
should be remembered that such changes are after all only a re- 
action. The formation of such circles can only follow an already 
existing and definite stratification of the economic system along 
the hues which we have suggested. Speaking more strictly, it 
must have been preceded by the choice of some area as the foun- 
dation of the economic system. This foundation must have been 
chosen as the agricultural basis within which the settlements of 
the non-agricultural population are afterward fixed.^ It is im- 

^ Cf . above, pp. xix ff. 

" It may be, as was said before, that the economic advantages of these non- 
agricultural settlements have been decisive in the choice of the area. But that 
does not alter the fact that they are only an incidental factor decisive in choosing 
the area as a whole, but not the primary factor in the process of its stratification. 


possible to conceive of this '^reaction" as anything but a sec- 
ondary phenomenon, although it is true that Thiinen did assume 
the city as the unexplained basic phenomenon of the distribution 
of agricultural locations. We, on the other hand, wish to clarify 
as far as possible just where and how cities develop. For this 
purpose we must go beyond the reaction of this growth of the 
city upon the distribution of the agricultural population; we are 
forced to analyze in the foregoing manner the process of strati- 


How far does this locational structure substitute real data 
for construed ones and thus fix the industries unequivocally ac- 
cording to the rules which we have found? Three construed 
data had to be replaced with real data: those relating to places 
of consumption, those relating to material deposits, and those 
relating to labor locations and their unlimited labor supply at 
constant cost (equal wage levels). 

I. Our entire analysis of the mechanism of stratification is 
built upon the idea of treating the different strata as spheres of 
consumption of their successors. The sphere of consumption is 
therefore throughout these strata something given, although of 
course variable in the upper strata in accordance with changes 
in the lower. In most cases this sphere of consumption is given, 209 
not as an indefinite geographical distribution of consumption, 
but rather as very definite places with very definite magnitudes 
of consumption. Certainly they were treated as definite places in 
the elaboration of our theory. And the sphere of consumption is 
in fact given in this definite form for all the higher strata, for 
which higher strata the places of production of the lower strata, 
as well as the centers of organization and trade, become places of 
consumption of a very definite magnitude. And what we have 
just said of the higher strata holds true even for the primary in- 
dustrial stratum which is built upon the agricultural stratum. 
While this is true, it certainly must be conceded that there are 


manifold agrarian forms of settlement which make for multi- 
farious structural developments of this basis of consumption; 
and it must furthermore be conceded that the connection be- 
tween this primary industrial stratum and the underlying sphere 
of agricultural consumption may be very difficult to detect, be- 
cause the rather scattered agricultural consumption cannot be 
supplied except via the agglomerations created by industrial pro- 
duction (cities). All these facts are only extraneous complica- 
tions which interfere with our perceiving that here also we have 
a system (a very complex one) of places of consumption having 
a given magnitude. The industries will orient themselves in ac- 
cordance with this system in exactly the same way (disregarding 
the ''reaction" we have discussed before) as they do in the higher 
strata where the forms of distribution of consumption are more 
clearly perceivable. 

2. The distribution of the material deposits takes place in 
terms of the system of places of consumption according to the 
rules which the theory has given for the construction of the lo- 
cational figures based upon the places of consumption as a start- 
ing-point — at least this is true of a large part of the material 
210 deposits which exploit deposits already in existence such as 
mines and the like. In such cases the choice of the material de- 
posits is all that has to be done, and this has been described in 
the theory. But the problem remains of how those material de- 
posits are located which are agricultural in nature, since in this 
case the "deposits" themselves must be "created," natural con- 
ditions being the only given factor. 

If there were no independent forces involved in the distribu- 
tion of agricultural production, the answer to this question would 
be simple. In that case we could say that the natural conditions 
of production of the materials are the determining factor, that 
the more or less favorable "natural conditions," in conjunction 


with their location, would determine the development of such 
"deposits" according to the same rules according to which the 
more or less favorable location of the already existing mining 
deposits determines their employment in conjunction with their 
productivity. In both cases these deposits would be given if the 
places of consumption were given. As a matter of fact the indus- 
trial strata do try to shape their basis of agricultural materials 
in a way analogous to their basis of mined materials, as some- 
thing given by their natural conditions. But industry will be 
thwarted in these attempts by the inherent tendencies of agri- 
cultural distribution, which tendencies of course affect the devel- 
opment of agricultural production in spite of the fact that it is 
the basis of industrial strata. In other words, the economic con- 
ditions of agricultural production will become a determining 
factor in addition to those which would be decisive if only the 
usefulness of agricultural production as an industrial material 
deposit were in question. Specifically, this involves its location 
in relation to the places of consumption and in relation to the 
labor locations as well as its rank among competing material de- 
posits. These conditions are of course the ones analyzed by 
Thünen,^° and as we have seen they are in part secondary phe- 
nomena of industrial stratification itself. In this case they touch 
the primary foundation. This shows that the actual develop- 211 
ment of these agricultural material deposits can only be regard- 
ed as given provided this circular process is introduced into our 
analysis, i.e., in the empirical analysis. But it is important that 
we know these rules and that we realize they do not contain any- 
thing problematical. As said before, the interference of the eco- 
nomic conditions of agricultural production means that the rules 
as set forth by Thünen become operative. Each agricultural 
material deposit is under competition from other agricultural 
employments which would use the soil for the production of 
different materials. The most profitable use will be the one un- 

^^ Cf . above, p. xix. — Editor. 


dertaken. For our purposes this fact may be expressed in the fol- 
lowing fashion : each industry will have as many potential de- 
posits of the agricultural materials it needs as there exists area 
which is by its nature capable of producing this material. But it 
will have these potential deposits at very different ''prices at the 
deposit." At each deposit the "price at the deposit" for a certain 
material is determined by the necessity of displacing the (ac- 
cording to Thiinen's law) next profitable employment. Thus 
these potential deposits are by this ''price at the deposit" placed 
into the scale of possible material deposits of their own kind 
much in the same fashion as the deposits of mining materials 
are. They will be developed as bases of locations and employed 
for production according to the rules we know. 

The places of consumption and the material deposits are 
given by the locational structure of the economic system as we 
have analyzed it. The rules which determine them are some- 
times quite direct and simple, sometimes a bit more complicat- 
212 ed, but in every case they are quite unequivocal. This means 
that the picture of the orientation of industry would be revealed 
(within the framework of the locational structure we have ana- 
lyzed) by the locational rules which we have discovered, if this 
orientation were independent of the labor locations and of the 
differences between their wage levels, and were based solely 
upon costs of transportation and the "pure" agglomeration built 
upon this transport orientation.^^ For to the extent to which 
orientation is determined by these forces, only the world of 
places of consumption and of material deposits comes under 
consideration as the given geographical basis of the real struc- 
ture. It would be possible to calculate for each geographical 
framework and for each stage of general economic and technical 
development how the locational picture of industry would shape 
up provided the number of population, the distribution of agri- 
cultural settlement, and the main distribution of the "central or- 

- Cf. pp. 135 ff. 


ganizing stratum" were known. There would be no room for the 
influence which a particular economic system (capitalism, so- 
cialism, or some other) could exercise upon the basic locational 
orientation, since the "pure" rules would fix the locations of in- 
dustry in a general way, at least. The theoretical task would be 
completed, and no further "reahstic" theory would be necessary. 


But what will happen if we take into consideration the de- 
viations due to labor and the labor orientation which rests upon 
them? The discussion of these deviations has thus far been 
based upon the assumption that the labor locations were given 
and that the differences in their wage levels were constant. Does 
the mechanism of local distribution which we have considered 
thus far give us any clues for determining the local distribution 
of such differences of wage levels, for the causes creating the 
labor locations, and finally for the rules determining their devel- 
opment which have so far been eliminated by the assumption of 
an unlimited supply of labor at equal cost? Apparently none 
whatever. This is the great gap in our analysis so far. In the 
rules determining the creation and the development of labor lo- 
cations lies hidden the problem which remains for a further the- 
oretical analysis. This problem will have to be solved by the 213 
"realistic" theory. For at this point it becomes necessary to con- 
sider particular economic systems. I do not wish to assert that 
the creation and development of labor location can be explained 
by economic reasons; but if it can be so explained the reasons 
will be related to the position which the particular economic sys- 
tem gives to labor. For apart from what one calls (according to 
Sombart) an "economic system," i.e., apart from the particular 
determining form of organization which the particular social 
concepts of a given time impress upon all economic relationships 
on account of which they appear as a part of a social order, all 
economic relationships are taken into consideration by our gen- 


eral analysis of a ''pure" economic system/- The further realistic 
theory must therefore consider how labor is handled in the par- 
ticular economic system which is studied. If we would exhaust 
the theory of location of industries of today, if we would explain 
fully the local grouping of the economic forces and the aggrega- 
tion of population, we must ask what it means for the local 
grouping of labor that labor is treated as a commodity. It will 
be seen that this circumstance determines about one-half of the 
local distribution of our present social system. 

" The interested reader may with profit consult Talcott Parsons, " 'Capital- 
ism' in Recent German Literature: Sombart and Weber," in Journal of Politi- 
cal Economy, vols. XXXVI-VII, and the Hterature cited there. Cf. also above, 
page 10, footnote, on the concept of an economic system. — Editor. 


Georg Pick 

Introductory remark. — Upon the suggestion of the author of this 
treatise I have attempted to outline in popular form some mathe- 
matical considerations which are necessary for an understanding of the 
problem of locations. Regarding sections I and II, I should like to 
refer to a recent treatise of Scheffers^ which gives the necessary mathe- 
matical aid for the solution of such problems. The formula of agglom- 
eration which forms the main part of Section III is stated in analogy 
to similar problems in different fields of apphcation. I wish that further 
formulas, particularly locational figures with more than three points, 
might be developed. But they stiU present some real difficulties.^ 


§ I. The locational triangle. — In the accompanying figure, A^ repre- 
sents the material deposit, A 2 the fuel deposit, A^ the place of con- 
sumption. Let us suppose that a^ tons of material and 02 tons of fuel 
are needed to produce a^ tons of the product (we shall assume a^ 
always to be i). If the place of production is located in P, at a distance 
of ri miles from ^1,^2 miles from A 2 and r^, miles from A^, then ^3 ( = i) 
tons of produce apparently require 226 

K = a^r^-{- 02^2 + a^^r^, 

ton-miles of costs of transportation. 

For which positions of P are these costs as small as possible? It is 
obvious at once that as long as P is situated outside of the locational 

^ As Mr. Bauer suggests, the whole case corresponds rather strikingly to certain 
parts of electrostatics, particularly equipotential surfaces. Cf. J. H. Jeans, The 
Mathematical Theory of Electricity and Magnetism, pp. 54 £f. — Editor. 

^ G. Scheffers, Funktionen der Abstände von festen Punkten (1900). 

3 For an attempted, though unsuccessful, solution of this problem, the reader 
may consult Launhardt, "Die Bestimmung des zweckmässigsten Standorts einer 
gewerbUchen Anlage." I have given a resume of the pertinent passage beneath, 
p. 238. — Editor. 




triangle Ä1A2A3, any approach of P to the side of the triangle next to 
F must result in shortening all three distances r^, ra, r^ and thus in 
lowering the costs of transportation. The locus of the minimum point 
cannot, therefore, lie exterior to the triangle. It lies either interior to 
the triangle or upon its boundary. We shall begin with treating the 
first of these two possibilities. 

§ 2. The minimum point in the interior of the locational triangle. 
Mechanical model. — The mathematical analysis of the necessary condi- 
tions'* or the point of lowest costs of transportation shows the following 

Fig. 44 

results. Let us imagine a variable point mass at P which is pulled with 
the force a^ toward ^i, aa toward A2, and a^ toward A^. The position of 
P for which these three forces are in equilibrium is the locus of the mini- 
mum point. 

This suggests that we might demonstrate the position of Pq (as 
we may call the point of least cost of transportation) by a mechanical 
model with an automatic device. This leads us to an old apparatus 

4 The necessary conditions of this case may be stated as f oUows : The function 
of the locus K has in its minimum point the differential quotient zero in all direc- 
tions : 




(for each direction of s). This formula gives us two equations for the necessary 
condition the significance of which is set forth in the text (cf. Scheffers, loc. cit.). 



which was invented by Varignon to demonstrate the parallelogram of 
forces. Upon the edge of a graduated circular disk three little rollers 
with horizontal axes may be affixed. Over each roller runs a thread. 
The three inner ends of the threads are coupled together at some point, 
the outer ends hang down and may bear little weights. In order to 227 
realize a given case, we shall first place the rollers so that they form the 
corners of the locational triangle. For this we can use the scale upon 
the edge of the circular disk. After this we load the three threads with 
weights proportional to the transport weights öi, «2, Ö3 for which we 

Fig. 45 

may substitute the same units of a small weight, e.g., dekagram. The 
connecting point will move by itself to the position of the minimum 

§ 3. Geometrical construction of Pq. The weight triangle. — Figure 46 
shows the forces Ö1, 02, «3, acting upon Po as straight-line segments 
whose length is proportional to the force. According to the theorem of 
the parallelogram of forces each of these straight-line segments if laid 
out from Po opposite its own direction will constitute the diagonal of 
the parallelogram formed by the other two straight-line segments pro- 
vided a state of equihbrium exists. If one lays out the three balanced 
forces (straight-line segments) following each other in their proper 
direction and length, a closed triangle (G1G2G3 of the figure) results. 




The angles of this triangle TiTzTs are the supplements of the three angles 
ßißzßs which are formed in Po by the straight lines connecting Pq with 
the corners AjA2Ay This may be seen by a glance at Figure 46. The 
triangle G1G2G3, which is fully determined in advance by its sides 
01^2^3 shall be called weight triangle. This weight triangle gives us the 
angles 71T2T3, and therefore ßißiß^. In order to find the point Po 
we shall have to determine that position of P from which the lines 
connecting P with y4i^2^3 form these particular angles, or, as one 
sometimes says, that position of P from which ^2^43 is seen subtending 
the angle ß^, A^A^, the angle JÖ2, ^1^2, the angle ßi. 

Fig. 46 

§ 4. Continuation. The three circles of construction. — In order that 
the angle A^PoA^ have the given size ß^, Po must he (according to 
the theorem about angles at the circumference of a circle) upon a cer- 
tain arc which stretches from A^ to A2. But Po must also He upon a 
corresponding arc ^2^3, because ^2^0^ 3 should have the given size 
jSi; and finally Po must lie upon arc AA^ because ^3Po.4i = jÖ2. Hence 
we only have to construct these arcs (two suffice), in order to get Po 
as their point of intersection (Fig. 47). 

In order to construct the arc through ^1^2 we have to apply the 
angle (/33 — 90°) to A^A^ at A^ and A2, so that an isosceles triangle re- 
sults, with its apex at C. (Fig. 48.) This apex C is the center of 
the required circle, which may therefore be constructed at once. 



Indeed it is A2CAi = iSo° — 2 (183 — 90°) = 360° — 2^83, and consequently 
the salient angle at C is equal to 2ß^, as was required.^ 

§ 5. Approach of the position of the minimum point to the boundary 
or to a corner of the locational triangle. — When does Po lie near one of 
the sides of the triangle, for example ^1^2^ 3? It is apparent that the 
angle AzPoA^, i.e., jSi will be almost equal 180°, and that 71 will be 
almost equal 0°. The weight triangle has therefore one very small 
angle; consequently the subtending side Ö1 will be very small, too, while 

Fig. 47 

the other two 02, Ö3, will be nearly equal. If öi becomes zero (and 
02 = 03), Po lies upon ^2^3. This is apparent anyway; for Aj has dis- 
appeared; the locational triangle has shrunk to a locational Hne (Fig. 


When does Po lie near a corner, for example A^? It is evident that 
in that case the angle ^2Po^3, i.e., jSi, will be almost equal to A2AiA^, 
that is, almost equal to the angle a^ of the locational triangle, while ßi 
would be noticeably larger if Po were located more in the center of the 
locational triangle. Similarly, 71, the supplement of ßi, is now almost 
equal to the supplement of ai (the exterior angle of the locational tri- 

s Instead of this construction, we may state the following rule : Erect a tri- 
angle similar to the weight triangle upon each of the three sides of the locational 
triangle. The circles described around these triangles are those required. 




angle at ^i) which would usually be considerably smaller. Hence as 
long as the angles of the weight triangle are smaller than the cor- 
responding exterior angles of the locational triangle, Po will He within 
the interior of the latter; but if one of the angles of G1G2G3, for example 
7i, is equal to the corresponding exterior angle oi A^AiA^, in this case 
i8o° — tti, then Po is located at the corresponding corner, A^. 

§ 6. Position of Po in one of the corners. The cases without a weight 
triangle. — We shall imagine now that the weight triangle G1G2G3 is 


Fig. 49 

undergoing changes, and see what changes of the position of Po result 
from it. 02,^3, shall remain unaltered, while öi is increasing gradually 
which causes the opposite angle 71 to increase also. We have just seen 
that Po goes to the corner A^, when 71 has reached the size i8o° — aj. 
What will happen if a^ and 71 increase further? Apparently Po remains 
in its position at ^i. For if the share of a^ is already so considerable 
that the transport from yli to Po must be avoided altogether in order 
to achieve a minimum of costs, it will be that much more necessary 
230 when the relative value of öi increases further. 

When the value of Ö1 has become equal to 02 plus a^, 71 has become 
equal to 180°, in other words the weight triangle has shrunk into a line 
(Fig. 50). If fli increases further, so that ai> 02+^3, no triangle can 


be constructed out of Ö1, Ö2, Ö3, and the weight triangle has ceased to 
exist. But still, Po lies at Aj.^ 

The model described in § 2 shows the right position of Po for these 
cases, provided that care is taken to prevent the connecting point of 
the three threads from sliding over the rollers. 

§ 7. Comprehensive recapitulation. Characteristics of the dißerent 
cases. — We may, then, distinguish three separate possibiH ties which may 
be characterized as follows : First, weight triangle exists, Po hes in the 
interior of the locational triangle; second, weight triangle exists, Po 
lies in one of the corners; third, weight triangle is lacking, Po lies al- 
ways in one corner. But while the third case can be recognized at once 

Fig. 50 

because of the impossibihty of constructing a weight triangle, it re- 
mains to give an additional characteristic in order to distinguish the 
first two cases. Let us recall the circles of construction in § 4. As long as 
Po lies in the center of the locational triangle, these circles intersect in 
the interior of the triangle, each of them excluding the corresponding 
third angle. If Po approaches the corner A^, the arc over ^2^3 passes 
near Ai, and if Po reaches A^ (because, as we have seen in § 5, 7i = 
i8o° — tti) this arc passes through Ai and intersects there with the 
other two circles. If 71 increases further, the arc subtending ^2^3 will 231 
go beyond ^i, so that Aj will come to lie in its interior. The point of 
intersection of the three circles now falls entirely outside of the loca- 
tional triangle. At the same time this point ceases to be a solution of 
our problem; for Po remains at ^i. The second case can be recognized 
by the fact that one of the circles of construction includes the third 
(i.e., that corner which does not he upon its base); in this case this 
included corner is always the minimum point. 

^ In these instances where Po lies in one of the corners, other conditions prevail 
those indicated in footnote 4. - 
Po, and usually not equal to zero at Po. 

J 7^ 

than those indicated in footnote 4. — is now positive in all directions from 


§ 8. The behavior of Pq when the weights ai, Ö2, ^3, remain unchanged, 
but the locational triangle changes. — We have investigated the changes 
of the position of Pq which are caused by changing the transport 
weights Ö1, 02, öj while the locational triangle remains unchanged. We 
shall now suppose öi, ^2, % fixed, while we change the form of the loca- 
tional triangle, and we shall observe how Pq acts under these condi- 
tions. Let us, moreover, suppose two corners, perhaps A-,, A2, fixed; 
only the third corner, ^3, shall move. 

Let us first take up those cases without a weight triangle, where 
one of the three weights d, aa, ^3 exceeds the sum of the other two. Ac- 

cording to § 5, Po hes at A^ when (Zi, at ^2 when Ö2, at ^3 when % is 
the large weight. Hence Po either remains unmovable at one of the 
fixed corners ^i, A2, or Pq participates in all movements of A^, always 
coinciding with this point. 

§ 9. Continuation. The center lies upon the circle through Ai, A2. — 
If the weight triangle exists, we can take from it the angle 73 and con- 
struct the arc over A^Ai as was shown in § 4 (Fig. 51). It is necessary 
to distinguish whether A^ Hes in the segment between the chord 
A1A2 and the arc or outside of it. The first case is identical with the 
second case mentioned in § 7 : Pq coincides with A^ If, however, A^ 
lies outside of the segment, then the construction shown in § 4 takes 


place, as we know in advance that Po will lie upon the arc A^Ai itself. 
The Hne connecting Po with ^3, together with the lines connecting Po 
with ^i and .42, forms (cf. § 3 and §4) the angles 1 80°— 72 and 1 80°— 71. 
Its extension backward beyond Po together with these lines includes 
the fixed angles 72, 7i. Wherever /I3 may be, Po will lie upon the arc 232 
through ^1^2, in such a way that the extension of A^Po together with 
Po^i always includes the same angle 71 at the point Po. According to 
the theorem regarding angles at the circumference of a circle, PqA^ 
will intersect the circle through A^,, ^2 in a fixed point {M of Fig. 51) 
which can easily be constructed. We only have to apply the angle 72 
at A2 to .42^3 downward, and the second side of this angle will inter- 
sect the circle in the required point M. 

This reasoning is correct as long as Po does not coincide with one 
of the points A-,, A 2. Because in these cases there is no longer any 
reason why A^, Po, and M should lie upon one straight line. Indeed, 
it is apparent that Po Hes alv/ays and only at ^i, if ^3 lies somewhere 
in the angular space whi ch fa lls between the extension of MAi beyond 
yli and the extension of A2A1 beyond Ai. The situation regarding A2 
is analogous. 

Let us imagine ^3 approaching AjA2 from a great distance along 
any line going through M. If the straight line upon which A^ is ap- 
proaching crosses the line going through A1A2 outside of the segment 
AiA2, Po lies fixed either in Aj, or in A2. But if it crosses between Ai 
and A2, Po lies at the point of intersection of A^M with the arc as long 
as A^ has not reached the segment of the circle subtending ^1^2. But 
as soon as ^3 enters into the interior of this segment, the point Po will be 
taken along and will always be combined with A^. 

While A^ changes its position in the entire half-plane above the 
straight line going through ^1^2, Po always remains confined to the 
interior and the boundary of the segment of the circle subtended by A1A2. 

§ 10. Survey figure showing the changes of transport costs when the 
position of A^ changes. — One and the same position of Po may cor- 
respond to very different positions of A^, as has just been seen. But 
total costs of transportation change with the position of Ay We will 233 
get a good view of this situation if we connect by a curve all those 
positions of A^ which show equal costs of transportation. These curves 
show (Fig. 52) a very different shape in the different parts of the half- 



plane extending above the straight Hne going through Ä1A2. In the 
before-mentioned angular spaces at Aj and A2 they are apparently con- 
centric arcs around Ai and A 2 respectively. In the main space lying 
between these two we have to distinguish again the segment from the 
exterior. Within the segments we get elHptic curves; but in the ex- 
terior one curve results from another if we move its points the same 
distance upon each of the straight lines through M. At the Hnes sep- 
arating the four spaces the curves appear broken. 


^, Curves of equal transportation costs, when 
-r^" one deposit is movable. If A^ goes from one 
P line to the next, the transportation costs in- 

crease to the extent of the straight line 

1^ 11 10 9 

8 9 10 11 12 

Fig. 52 

§ II. Two locational triangles in mutual relation. — ^Two locational 
triangles A^AzA^ and ^MMa shall be related in such a way that A^ 
is at the same time the place of production for the first triangle and A^ 
at the same time the place of production for the second triangle. In view 
of this quality we shall designate these points as Po, Po- We shall as- 
sume the locations A1A2 and ^3^2 and the two sets of weights a^, 02, 
«3 and a'l, a'2, a'^ as given. The points required are Po = ^i and Po = ^3 
in such a position that total costs of transportation become as smaU 
234 as possible. Those cases in which no weight triangle exists in one of 
the two locational triangles are extreme cases. If this is, for example, 
the case with regard to the first set a^, 02, Ö3, then Po=Ai must lie 
combined either with Aj, or A2 or with A.=Fo. We therefore either 



have A'l given at once, or the two places of production are combined, 
which would mean that one place of production for four given points 
would have to be found. Separate places of production located else- 
where than in the given points are only possible, therefore, if both 
weight triangles exist. Under this condition the two segments sub- 
tending AjAz and A'^Az exist as has been discussed in § 9. We get the 


\ /I 
\ / 1 

\ / 

'i / 

\ / 


i' / 


Fig. 53 

two points M and M'. If we connect therefore M with M', the con- 
necting line will cut the two circles at the required points (Fig. 53). 

But this rule is subject to several limitations. If the segments over- 
lap in part, and MM' traverses the common part, then Po and P'o are 
combined (according to § 9) and may not lie upon MM'. We get again 
the case of one place of production with four determining points. If, 


on the other hand, MM' does not meet one of the segments at all, then 
■ Fo or P^ will Ue in one of the corners A^, A2 and A'^, A2 respectively 
(cf. Fig. 52) ; in other words, either P« or P^ are given at once and the 
remaining problem reduces itself to the fundamental problem. The 
exceptions are therefore of a more simple nature than the regular case 
for which construction Figure 53 brings the solution. 
235 § 12. Locational polygons with more than three corners. — In spite of 

the fact that generally speaking the essential part of the problem and 
the principles of its treatment are unchanged in the case of locational 
figures with more than three corners, it is impossible to give equally 
simple rules for construction even in the next higher case of the quad- 
rangle. It is' worth noting that the mechanical model functions in aU 
these higher cases (if properly adapted). For if we let weights corre- 
sponding to the sets of transport weights pull threads at the corners 
of any locational figure, the point at which these threads are coupled 
together will automatically go to the minimum point. ^ 

7 Cf . for the contrary opinion, Launhardt, "Die Bestimmung des zweckmässig- 
sten Standorts einer gewerblichen Anlage," in Zeitschrift des Vereins Deutscher In- 
genieure (1882), pp. 107, iio-ii. In this short essa}- Launhardt is concerned mth 
figuring out the most favorable location of an isolated process of production which 
uses only localized materials. Although this is a very narrow and limited aspect of 
the problem of industrial location, it seems desirable to give a short resume of his 
geometrical arguments, because they lead him to the conclusion that the construc- 
tion of minimum points is possible for polygons with any number of corners. 

After having arrived at the conclusion that "the kilometric costs of transporta- 
tion must hold each other in balance at the location of production," he finds the 
minimum point by constructing a triangle similar to the weight triangle upon the 
side A1A2 of the locational triangle. He then describes the circle around this triangle 
and connects the third corner O of this triangle with the third corner of the loca- 
tional triangle, A^ (it will be observed that this involves the simpnf3dng assumption 
that A^ is always the center of consumption, while the reasoning of Pick is entirely 
independent of the question as to which of the three points is the center of con- 
sumption) . The point Po at which this connecting fine intersects the circumference 
of the circle is the required minimum point. Launhardt calls the point mentioned 
above the "pole" of the locational triangle. 

Using the theorem of Ptolemy, Launhardt proceeds to analyze locational 
polygons with the aid of his construction of a "pole" (cf. Fig. 53A). He thus re- 
places both Ai and A2. This substitution of the pole O for ^i and A2 becomes the 
basis of his construction of the minimum point for a quadrangle, Ax A2 A^ A^/io. 
which ^3 is again fixed as the place of consumption. What he does is simply to 


Even for distinguishing the cases where the minimum point P^ lies 
in the interior from those cases where it Hes at the corners of the loca- 
tional figure, we do not have those simple criteria which we had in the 
case of the triangle. Suffice it to indicate that Po will apparently lie 
at one of the corners, if the weight of that corner equals or exceeds the 
sum of all others (Fig. 54). 

construct a "pole" for A2 and A^, and then construct another "pole" for Ai and 0. 
The line connecting this second pole Q with A^ will, Launhardt believes, give the 
minimum point Po where it intersects the circle described around the triangle AiQO. 
Launhardt does not attempt to prove his contention. It appears to be wrong. 
Neglecting the (rather important) circumstance that it is not apparent just on 


Fig. 53 a 

what basis these two poles are constructed (inasmuch as in the fundamental 
case of a triangle they were found by constructing a triangle similar to the weight 
triangle which does not exist here, since we are dealing with a quadrangle), the 
obvious objection to it is that it involves a detour, and therefore additional costs 
of transportation for the materials coming from A2 and ^4 to P. It is difiicult to see 
how, in view of this fact, it could have escaped Launhardt's attention that he was 
not reaUy getting a minimum point at aU. Moreover, he himself observed that a 
second and different solution is possible. This, he says, is achieved by constructing 
first a "pole" O' for the points Ai and A^, and by then determining the location Po 
for the remaining points A^, A2 and O' through their "pole" Q' . Was this fact in 
itself not an indication that the real minimum point lay somewhere in between 
these two? There is, as a matter of fact, still another and third possibility, namely 
to begin with Ai and A2. 

It is surprising that Bortkiewicz, in his review of Weber's theory {Archiv für 
Sozialwissenschajt und Sozialpolitik, 19 10) should not have noted these fundamental 
limitations and errors in Launhardt's essay when he, at the same time, asserted 
that Launhardt had done before what Pick is setting forth in this Appendix. — 



§ I. The concept oj the isodapanes. — If in any locational figures the 
transport weights fl« are known and the minimum point Po ascertained 
and still the place of production is not located at Po, then costs higher 
than the minimal costs will be incurred. It is imaginable that the place 
of production gradually moves away from Po in any and all directions. 
In every direction the costs of transportation will rise gradually and 
may reach any amount, provided only we move the place of produc- 
tion far enough away from Po. Smaller costs of transportation than in 

Fig. 54 

Po of course cannot be found anywhere; but it is obvious that we shall 
be able to find loci for any amount of transport costs higher than those 
238 in Po, and we will be able to find such loci in every direction from Po. 
Consequently there exists not only one such locus, but a closed curve 
around Po which consists of all the loci having equal costs of trans- 
portation. Such a curve (curve of equal transport costs, level curve of 
transport costs, isodapane) will exist for any value of total transporta- 
tion costs, provided only that such value is higher than the minimum. 
The totality of these curves gives a clear picture of the way in which 
the transport costs depend upon the location of the place of produc- 
tion. If the minimum is M ton-miles, we may draw the isodapane for 
each additional 10 ton-miles; in other words, those curves upon which 
the costs of transportation would be M-{-io, M-\-2o, M+30, etc., 
ton-miles (cf. Figs. 55-58). 

§ 2. Isodapanes for very high values of costs are approximately circles. 
— Very high transport costs have loci which are very far away from 
Po and the locational figure too. If this distance is so considerable that 



the dimensions of the polygon appear insignificant, then that distance 
becomes the only determining factor. Hence those curves which cor- 
respond to very large costs of transportation will not differ very con- 
siderably from large circles around Pq as center. If the radius of such 

Fig. 55. — Isodapanes I. Ratio of weights: 3, 4, 5. The minimum costs of 
transportation are represented by Mo, their increment from one isodapane to the 
next by m. 

a circle is R, the transport costs for some location of the place of pro- 
duction upon its circumference are approximately equal to 

i?(ai+Ö2+Ö3+Ö4 . . . .) ton-miles, 

because it is admissible to assume without noticeable error that all 
locations are united in Pq. If we designate the sum 


that is the total weight which has to be moved for the production and 
distribution of one ton of product, as G (locational weight), we can 


Fig. 56. — Isodapanes II. Ratio of weights: 3, 4, 6 


Fig. 57.— Isodapanes III. Ratio of weights: 3, 4, 8 



formulate the following rule: The transport costs for places of pro- 
duction very far away from the locational figure are to be found by 
multiplying the locational weight with the distance of the place of pro- 
duction from the minimum point: GXR. 

If the isodapanes are drawn for a certain gradation of the trans- 
portation costs, as indicated in i, these large circles will he the closer 
the larger the locational weight is. For the larger G is, the smaller is 

Fig. 58. — Isodapanes IV. Ratio of weights: 3, 4, 12 

the increment of R which is necessary for causing the same increase of 

§ 3. Smaller values of the transport costs. The descent of the transporta- 
tion costs. — If we pass now to smaller values of the transport costs, the 
corresponding isodapane will run closer round the locational figure. At 
the same time the shape of the locational figure and the distribution 
of the sets of weights Ö1, ^2, a^, . . . . between the several corners will 
exert an increasing influence upon the shape of the isodapane, which 
wiU differ from the shape of a circle the more, the less the transport 
costs exceed the minimum, i.e., the closer the isodapane runs round 
Fo. Under all circumstances the system of curves which we have drawn 
will show us the following: If we transfer the place of production from 
one isodapane to the one next farther away from Po, we shall increase 



the transport costs by lo ton-miles. It follows that if we leave an 
isodapane in the perpendicular direction away from Po, the transport 
costs increase, and they do so the faster the nearer the next isodapane 
is to the one left. If, for example, the distance from the next isodapane 
is 5 miles, these 5 miles cause an increment to the transport costs of 
10 ton-miles; if the distance had been 10 miles, we would get the same 
increment of costs only after 10 miles. In the first instance the addi- 
tional costs for I mile are 2 ton-miles. If we caU the amount by which 
the transport costs are increased when the place of production is moved 
away from Po i mile in a perpendicular direction, the descent of the 
transport costs, we can derive the following rule for the determination 
of this value: Divide ten by the distance of adjoining isodapanes.* 
The closer the isodapanes follow each other, the larger is this descent. 

§ 4. Illustration by a spatial model. {Surface of transport costs.) — Let 
us imagine that we had raised a perpendicular straight line at each 
possible position of P in the plane, giving this perpendicular line the 
length corresponding to the sum of transport costs at the point where 
it is raised. In this way we shall get above each position of P a point 
240 in space, and all these points together constitute a surface. The lowest 
point of this surface lies above the point Po; right around it the surface 
rises, and at a certain distance from P« it does not differ very noticeably 
any longer from a conical surface whose vertical axis goes through Po, 
although it shows an irregular shape around the lowest point. If we 
go along upon this surface in such fashion that the distance above the 
ground plain remains unaltered, we shall be moving along an isoda- 
pane. The steepest ascent at any particular point is given by the line 
which runs perpendicular to this isodapane. The steeper the ascent is, 
the faster do the costs of transportation increase if we move away 
from the isodapane in a perpendicular direction. The steepness gives 
an immediate picture of the descent of the transport costs. 

5. The picture of the system of isodapanes in the immediate neigh- 
borhood of Po. — In the immediate neighborhood of Po the distribution 
of the isodapanes, and in connection therewith the shape of the surfaces 
of transport costs, differ widely, in accordance with the main cases 

8 Such inexact explanation of this concept may suffice here. In truth what is 
involved is the differential quotient (taken with the inverse sign) -^ of the trans- 
port costs in that direction in which K decreases fastest. 


given in I, § 7. If Po lies in the interior of the locational figure, the first 
isodapane following Po (given fixed gradation, e.g., the 10 ton-mile 
increment) will be fairly far away from Po on all sides, due to the fact 
that strictly speaking the descent has the value zero in Po. The same 
is true when Po is located in one of the corners, as long at least as the 
corresponding weight does not exceed the sum of the others consider- 
ably. But it appears at once that the first isodapane, in so far as it runs 
outside of the locational figure, runs much closer to Po than it does in 
the interior. But if the weight attached to the particular corner be- 
comes very considerable, the first isodapane approaches the point Po 
correspondingly from all sides, so that it surrounds it closer as the 

M\ \m 

Fig. 59 

weight of that comer increases as compared with the sum of the others. 
The surfaces of transport costs will in the first case have the shape of a 
very shallow depression which in the case of location in the corner wiU 
be somewhat steeper outside than inside of the figure. In the case of 
considerable weight at one corner, however, the surfaces will exhibit 
a more or less steeply funnel-shaped depression. The Figures 55-58 
will give a clear idea of all these aspects, since they correspond to our 
different assumptions. 


§ I. The function of economy and its diagram. — A large unit of pro- 241 
duction having the daily quantum of production M wiU absorb (ag- 
glomerate) a small unit of production of the same kind having the 
daily quantum of production m and lying at the distance r, if the econ- 
omies resulting from the agglomeration are greater than the resulting 
increase of costs of transportation. The latter is easy to calculate. If 
A is the locational weight of production, the additional costs for one 
ton of product apparently amount to ^r ton-miles. The total addi- 
tional cost amounts to Arm ton-miles, or Arms money-units, if 5 is 
the transport rate. 

The economies which result from agglomeration depend upon the 
kind of production. For each species we may imagine that we had set 
down in a tabular form the economies per ton of daily product which 



occur for each and any amount of agglomeration. Such economies are 
caused by the quantum of agglomeration M; they are a function of M. 
We shall call it the function of economy {M). Instead of giving it in 
the form of a table, as just mentioned, we may present it very clearly 
by a geometrical figure. Let us lay out the values M from the point 
of intersection of two axes perpendicular to each other. These straight 
line segments M are called abscissae. Then we raise a perpendicular at 
the extreme point of each abscissa and give it the length of the cor- 
responding function of economy {M). These lines are called ordi- 
nates. By this operation we get points in the plane which together 

Fig. 60 


constitute a curve, which presents the total course of the function of 

§2. The basic formula of agglomeration. The function of agglomera- 
tion. — If M is the quantum of a large unit of production, the economies 
produced by agglomeration will be (M) for each unit of product, and 

M <j>{M) 

for the daily product. 

If the small unit of production having the quantum of production 
m is combined with the larger unit, we shall get total economies 
amounting to 

{M-{-m)4){M-\-m) . 


Accordingly the increase of economies due to agglomeration is 
(M+ w)(/)(M+w) -M<t>{M) . 

As long as this value is larger than the increase in costs of transporta- 
tion, Arsm (cf. above), the agglomeration will actually take place. We 
get therefore the following equation for calculating the largest distance 
R to which the absorbing force of the large unit of production extends: 

ARs = 



The right side of this equation contains M as well as m. If m were at all 
considerable, it would indeed have an influence upon the magnitude 


Fig. 61 

of R. But the nature of the problem under discussion involves that m 
is a very small quantity as compared with M. In view of that the right 
side of the equation becomes quite independent of m, it becomes a 
function of M alone; but let us imagine for once that the equation con- 
tains first the value m and then twice the value 2m. In Figure 61 we 
see three rectangles incasing each other. Their area apparently is 

M<f)(M), (M+m)<t>{M+m), (M+2m)4>{M-\-2m) , 

respectively. Their differences, figures of a kind which the ancients 
called gnomon, are decisive for the previously given quantities. The 

big gnomon 



apparently approaches being twice as large as its part 

{M-^m)<i>{M-\-m)-M(j>{M) , 

243 as m decreases. This gives us 

(M+ 2m)(t){M+ 2m)-M4>{M) ^ {M-\-m)4>{M-\-m) -M(t)(M) 
2m m ' 

and this equation is the basis of the independence which we have 

The function 

.^. ^ {M^m)4>{M^m)-Mcf>{M) 

shall be called the function of agglomeration. Our previous formula 
is now transformed into 


and this is the basic formula of agglomeration. It shows that the 
radius within which the agglomerating force of a production of the 
quantum M is effective, is directly proportional to the value of the 
function of agglomeration, while it is inversely proportional to the 
locational weight and the transport rate. 

§ 3. Diagram of the function of agglomeration. — In order to get a 
clear survey, we shall imagine now that the function of agglomeration, 
as the function of economy before, is presented in a diagram (Fig. 62). 
In this diagram the perpendiculars upon the axis raised at the extreme 
points of the several M have the length /(JW). Above a small segment 
having the length m which has been laid out from the extreme point 
of M, there lies a strip of plane. This plane is bounded on both sides 
by the ordinates/ (M) and/Cilf+w) and on top by the curve of our 
diagram. We will be able to calculate this strip as a rectangle ha\dng 
the base m and the altitude f{M) the more accurately the smaller m 
is. This strip had the area 

244 mf(M) = {M-\-m)<l){M+m)-M4>{M) , 

and thus represents the increment of daily economies which results 
when agglomeration progresses from the values M to the value M-\-m. 



If we now look at the entire plane above the abscissa M which is 
bounded by the curve of the diagram and the ordinates, we can see 
that it is possible to conceive it as being divided into a whole series 
of strips. The value of this plane is, therefore, nothing but the sum 
of all the increments of economies from the beginning of the process of 
agglomeration up to the altitude M; in other words, the total econ- 
omies of agglomeration at M. It equals 

Mc}>{M) . 

Finally we may even get an idea of (f){M) itself. Let us imagine (Fig. 
62) the two axes and the ordinate of M being impermeable walls and 

f — 

1 1 ' 

1 1 1 
1 1 ' 


'.I \ .u 

M M+m 

Fig. 62 

the plane just mentioned as consisting of inflexible metal bounded 
in front and in back by parallel plates. If the metal would be liquefied 
now, it will readjust itseK so as to have a horizontal surface. Since the 
area of the resulting rectangular figure is M0(M), and its base is M, 
the altitude gives us 4){M).^ 

9 Higher mathematics will express the relations which we have discussed and 
which exist between the function of economy and that of agglomeration by saying: 
The function of agglomeration is the differential quotient of the function of economy 
multiplied by M: 





§ 4. Agglomeration of small units of production which have been uni- 
formly distributed. — Let us imagine small units of production which are 
distributed uniformly throughout a certain area. If a large unit of pro- 
duction develops within this area it will absorb the existing smaller 
units within a certain radius. If we wish to calcu- 
late the radius with the help of our formula of 
agglomeration, we must keep in mind that M itself 
changes and increases under the influence of the 
process of agglomeration. We designate as p the 
amount of daily production which is produced per 
jTjQ 53 unit of area under the original uniform distribution. 

245 This we shall call density of production. If then 

(Fig. 63) a large unit of production at G has absorbed all production 
just up to the circumference of the circle with the radius R, it must 
have reached the quantity 

ttR' p. 

Therefore this value for M must be introduced into the formula of 
agglomeration, or R must be calculated from 

ttR^ P=M : 

and then introduced. We thus get 

ARs=f{TrR'p) , 

or respectively 




From this equation we shall have to calculate M. This is of course 
possible only if the function of agglomeration f{M) is known. But if 
we have found the value of M, the quantum of agglomeration, then it 
is easy to give the approximate number of large units of production 
which have come into existence in the area dealt with. For if ß indi- 
cates the amount of daily production in the entire area, the number will 

apparently be 





§ 5. Ascertaining the quantum of agglomeration through the diagram 
of the function of agglomeration. — According to what has been said the 
problem is now to determine M in such a way that 


VM=f(M) . 


We shall imagine that we had laid out a second curve in the figure 

which contains the graphic presentation of f{M) by co-ordinating to 

each abscissa M the ordinate 




(Fig. 64). The points which we get compose a well-known curve, 
called parabola. The required abscissa is that abscissa for which the 


Fig. 64'° 

curve off(M) and the parabola have equal ordinales; in other words, where 
both curves meet. 

There exist several possibilities. The curve oif(M) may right from 
the beginning extend beneath the parabola and remain beneath it. In 246 
that case the equation is never fulfilled and always 

N}f(M) , 

'° For brevity's sake the designation 2p= is used for the so-called param- 


eter {2p) of the parabola. 


which means obviously that the increments of transport costs are 
never reached by the economies of agglomeration for any quantum of 
agglomeration. In this case agglomeration is impossible. 

Second, the curve of f{M) may in the beginning run above the 
parabola and then cross it at some place remaining beneath it after 
that. In this case agglomeration will occur up to that quantum which 
is indicated by the abscissa of the point of intersection of the two 

The third case in which f{M) runs from the beginning and always 
above the parabola does not, it seems, correspond to any actual cases. 


Agglomeration, xxi, xxvf., xxvii, 20 ff., 
24, 35; Alfred Weber's theory of, 124- 
72; analysis of agglomerative and 
deglomerative factors, 124-34; causes 
of, 3, 6; definitions, 126 f. Mathemati- 
cal considerations of, 245-51; and 
stages of production, 186 f. See also 
Laws of agglomeration; Realities, re- 
introducing the 

Agricultural basis of industry, 37 f. 

Agricultural production, theory of, xiv, 
xviii, XLX, XX, xxLx f., 5 ff. 

Assumptions, Weber's simplification of, 
37-40; the assumption of a separate 
basis of material supply, consump- 
tion, and labor, 37 ff.; the considera- 
tion of the "forces of nature," 39 f. 

Automobile transport, its effect upon 
location, 86 n. 

Bauer, Paul S., viii, 227 n. 
Böhm-Bawerk, E., 27 n. 
Bücher, Karl, 10 n., 190 n. 

Capital. See Fixed capital 

Capitalistic economic order, 26 

Chamberlin, E. H., vii 

Chapin, F. Stuart, 14 

Clark, A. B., xxviii n. 

Clark, J. M., xvii, xxvii, 46 n. 

Coefficient of manufacture, 162-66 

Competition: of price, 19; of quality, 
18 f. 

Cost: elements of, 28 ff. See also Labor 
cost, Production cost. Transportation 
cost of production and labor cost, xii 

Cultural factors and orientation of in- 
dustry, 21 f. 

Daggett, Stuart R., xxviii 

Deglomerative factors and orientation 
of industry, xxi, xxvf., 20 ff., 24, 
131 ff. See also Agglomeration 

Distribution, process of, 4, 5, 25 ff.; con- 
sumptive, 4; productive, 4 

Distributive process, 18 ff. 

Economic system or order. See System 

Economy, function of, 162 ff. 

Elliot, WüUam Y., vii 

Engländer, Oskar, xxii n., xxvii n., 
xxviii n., 51 n. 

Enviromnent, 14; and labor orientation, 

Equilibrium: in constructing minimum 
point, 229; of location, 213; in Mar- 
shall, xiv 

Fixed capital, 25 ff., 30 
Formkoeffizient ("the coefficient of manu- 
facture"), 162-66 
Free trade, doctrine of, xxviii ff , 

"General expenses," 28 

General factors of location. See Loca- 

tional factors 
Geographical factors and orientation of 

industry, i, 21 f., 24 

Haig, R. M., 17 n. 

Halbfabrikat, 174. See also Product 
HaU, F. S., xvii 
Haurath, John J., 172 n. 
Hoover, Herbert, xi n. 

Index of labor costs, 106-8. See also 
Labor index 

Index of manufacture, 164 ff. 

Insurance. See General expenses 

International distribution of industrial 
location, 15 

International tariffs and theory of loca- 
tion, xxvii f . 

International theory of labor, xxviii 

Isodapanes, 102-4, 122, 144 ff. 

Jeans, J. H., 227 n. 

Krzyzanowski, Wytold, xvii n. 

Labor cost, xxiff., 20, 21, 27, 28, 33; 
analysis of, Weber's theory of, 95- 




loi; and cost of production, John 
Stuart Mill's consideration of, xii; 
and rent, Thiinen's theory of, xix 

Labor index, xxii. See also Index of 
labor costs 

Labor organization, development of, 
129 f. 

Labor orientation, 95-123; agglomera- 
tion and, 156-62; and the stages of 
production, 184-86. See also Labor 
costs, analysis of; Laws of labor 

Land rent. See Rent; also Theory of 

Lardner, xvi n. 

Launhardt, 227 n., 238 n. 

Laws of labor orientation, 102-23; char- 
acter of the industries and labor orien- 
tation, 107-17; conditions of labor 
orientation, 105-7; environmental 
conditions of labor orientation, 117- 
20; isodapanes, 102-4; orientation of 
an entire industry, 11 2-1 7; orienta- 
tion of an individual plant, 107-12; 
tendencies of development, 120-23; 
theoretical solution, 102-4 

Laws of agglomeration, 134-62; ag- 
glomeration in the case of an increas- 
ing index, 143-47; agglomeration with 
fixed index, 135-43; agglomeration 
and labor orientation, 156-62; ag- 
glomeration within transport orienta- 
tion, 135-56; conditions of agglomera- 
tion, 147-53; formula of agglomera- 
tion, 153-56 
Laws of industrial location, 10 
Laws of transport orientation, 48-75; 
cases, 61-67; factors of the transport- 
orientation, 7 2-73 ; location figures and 
kinds of industrial materials, 48-53; 
material index, locational weight, and 
theoretical conclusion, 59-61; mathe- 
matical solution, 53-59; orientation of 
an entire industry, 67-72; tendencies 
of development, 73-75 

List, Friedrich, xxix 

Location, theory of, in relation to theory 
of land rent, xi-xxxi 

Locational factors and locational dy- 
namics, 17-36; agglomerative factors, 
20 ff., 24; ascertaining the general fac- 
tors of location, 21-34; classification 

of locational factors, 20-23; deglomer- 
ative factors, 20 ff., 24; explanation of 
terms, 17-20; general factors, 24; 
"locational factor," definition of, 18; 
"locational unit," definition of, 18 f.; 
regional factors, 20 ff., 240., 34; spe- 
cial factors 20; theory of the locational 
factors, 34-36 

Locational figures. See Laws of trans- 
port orientation 

Locational unit. See Locational factors 

Locational weight, xxii, 108-12, 150 f., 
155 f., 162 ff. See also Laws of trans- 
port orientation 

Locus of least cost of transportation, 

Manufacturing industry in the total 
economic system, 211-26; historical 
distribution of locations, 213 ff.; the 
result and the remaining problem, 
221 ff; the strata of locational dis- 
tribution and their interaction, 214 ff. 

Marketing factors, 130 f., 206-9 

Marshall, Alfred, xiii ff ; xxix 

Marshall, Leon C, vii, viii 

Mason, Edward, vii 

Material index, xxii. See also Laws of 
transport orientation 

Materials: cost of, xxi, 25 f., 28, 32 f.; 
kinds of industrial, 48-53; and pro- 
ductive processes, 201-6 

Mathematical Appendix (by Georg 
Pick), 227-52; agglomeration, 245-51; 
lines of equal transportation costs, 
240-45; the locus of least cost of 
transportation, 227-39 

Mathematical solution. See Laws of 
transport orientation 

Mill, John Stuart, xi-xiv 

Minimum costs. See Points of minimum 

Minimum point. See Points of minimum 

Monopoly and theory of location, xxvii 

National disposition, 14 
Natural factors and orientation of indus- 
try, xxix, 21 ff. 

Ohlin, Bertil, xxviii n. 
Orientation. See Total orientation 



Parsons, Talcott, vii, 226 n. 

Pick, Georg, viii, 227 ff. 

Pigou, A. C, xi, xxvii, 42 n. 

Points of minimum costs of transporta- 
tion, 53 ff. ; when location is split, 

Political interferences, 14 

Power, cost of, xxi, 25 f., 28, 32 f.; use 
of water power, 89-94 

Predöhl, Andreas, vii, xxiv, xxvii n., 
163 n., 172 n. 

Price, elements of, 26 ff. 

Price differences of materials and their 
effect, 88-89 

Price levels of deposits of materials, 34 

Product : half-finished, 1 74 f . 

Productive advantage, 18 ff. 

Productive process, 18 ff.; and distribu- 
tion process, 25 ff.; interaction of the 
independent, 196-21 1; organization of 
the stages of a given, 174-96 

Produktionsstufengliederung, 173, See 
also Stages of production 

Profits, 28 

Raw materials, location of, xii, xxi, xxxi, 
19, 20, 32 f. 

Real estate, 25 ff., 31 f. 

"Realistic" theory, 12 f. 

Realities (agglomeration), reintroducing 
the, 162-72; coefficients of (value add- 
ed through) manufacture (Form- 
koeßzient), 162-66; forms of ag- 
glomeration in reality, 166-67; tend- 
encies of development, 168-72 

Realities (total orientation), reintroduc- 
ing the, 187-96 

Reality (transport orientation), approxi- 
mations to, 76-94; different kinds of 
transportation systems working to- 
gether, 82-87; a divided transporta- 
tion system, 81-82; existing system of 
transportation rates, 76-81; further 
application of theory to reality, 88-94; 
price differences of materials and 
their effect, 88-89; real nature of the 
transportation system, 84-87; use of 
water power, 89-94 

Regional factors and orientation of in- 
dustries, xxi, 20 ff., 24 ff., 34, 124 

Rent: cost of, 20, 21; land rent, theory 

of location in relation to theory of, 
xi-xxxi; Marshall's theory of, xivff.; 
Mill's analysis of, in its relation to 
value, xiii; Thiinen's theory of, xLx. 
See also Real estate 

Ricardo, xii, xiv, xvii 

Ritschl, Hans, xxx n., 172 n,, 214 n. 

Roscher, W., xvii, 6 

Ross, Edward A., xvii 

Salin, Edgar, xiv n., xvii n., 172 n. 

Sax, Emil, 41 n., 46 n. 

Schaeffle, Albert E. F., 6 

Scheffers, G., 227 n. 

Schlier, Otto, 171 n. 

Schumpeter, Joseph, xi n. 

Shipping costs. See Transportation costs 

"Situation rent," xv 

Smith, Adam, xi, n. 5, xiv 

Social factors and orientation of indus- 
try, 21 ff. 

Sombart, Werner, xxiii, 38 n., 225, 226 n. 
Sorokin, P., 14 
Sprachgeist, vii 

"Stages" of production and transport 
orientation, 1 74 ff . 

"Stock" of industrial workers, 14 
System, the economic: its relation to 
labor orientation, 225; its relation to 
the location of industry, 211 ff.; its 
relation to locational factors, 26; as a 
theoretical concept, 10 n. 

Taussig, Frank W., vii, 42 n., 43 n., 46 n. 

Taxes. See General expenses 

Technical equipment, development of, 
128 f. 

Technical factors and orientation of in- 
dustry, 21 ff. 

Theory, economic, i ; its relation to basic 
assumptions in theory of location, 
211 n.; its relation to the concept of a 
"pure" system of economics, ion., 225 

Theory of location: importance of an 
economic theory, i; limitation to a 
theory of the location of manufactur- 
ing industry, and reasons therefor, 3; 
methods employed, 6; results, limita- 
tions of, 12 ff., 212 ff. 



Theory of location in relation to theory 
of land rent, xi-xxxi; in Alfred Mar- 
shall, xiii-xxx; in John Stuart Mill, 
xi-xiv; in J. H. von Thiinen, xiii, 
xviii-xxiii, xxvi, xxvii, xxix, 2, 5; 
in Alfred Weber, vii, viii, xi, xvi, 
xviii, xx-xxx; significance for a theory 
of monopoly transportation rates and 
international trade, xxx 

Theory of the locational factors, 34-36 

Thiinen, J. H. von, xiii, xviii-xxiii, 
xxvi, xxvii, xxix, 2, 5, 31 n,, 38 n., 
215 n., 220, 223 

Total orientation, the, 173-210; inter- 
action of the independent productive 
processes, 196-210; organization of 
the stages of a given productive 
process, 174-96 

Transport orientation, 41-94; agglomer- 
ation within, 135-56; and the stages 
of production, 173-83. See also Laws 
of transport orientation; Reality, ap- 

proximations to; Transportation 
costs, analysis of 

Transportation costs, xii, xviii, xxiff., 
20, 21, 27 f., 33, 34 f., 150; analysis of, 
41-48; locus of least cost, 227-39 

Transportation rates and theory of loca- 
tion, xxvii f . See also Transportation 
cost; Reality, approximations to 

Transportorientierung. See Transport 

Value, John Stuart Mill's consideration 
of, xii ff . 

Wages. See Labor cost 

Water power, use of, 89-94 

Water supply, 20 

Weber, Alfred, vii, viii, xi, xvi, xviii, 

Wissler, Clark, 14 n. 


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