ORI GIN AL PA PER
The early diffusion of the steam engine
in Britain, 1700–1800: a reappraisal
Alessandro Nuvolari • Bart Verspagen •
Nick von Tunzelmann
Received: 2 August 2008 / Accepted: 14 February 2011 / Published online: 5 March 2011
 The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract We examine the diffusion of steam technology across British counties
during the eighteenth century. First, we provide new estimates for the regional
variations in the timing, pace and extent of usage of steam engines. Our main data
source is an updated version of the list of steam engines erected in Britain during the
eighteenth century originally compiled by Kanefsky and Robey (Technol Cult
21:161–186, 1980). Following a rather established approach for analysing the dif-
fusion of new technologies we fit S-shaped growth functions to the data on the
numbers of steam engines installed in each county. In this way, we are able to provide
a comprehensive appraisal of the relative speed of the diffusion process in different
counties. Second, in order to assess the relative importance of the variables shaping
the diffusion of steam power technology, we study the relationship between the
number of steam engines installed in each county and localization factors such as coal
prices, availability of water sites, number of textile mills and number of blast furnaces.
Keywords Steam engine  Diffusion  Great Britain  Industrial revolution
JEL Classification N73  O14  O33
A. Nuvolari (&)
Laboratory of Economics and Management (LEM),
Sant’Anna School of Advanced Studies, Piazza Martiri della Liberta` 33, 56127 Pisa, Italy
e-mail: alessandro.nuvolari@sssup.it
B. Verspagen
Faculty of Economics, UNU-Merit, Maastricht University,
P.O. Box 616, 6200 MD Maastricht, The Netherlands
e-mail: b.verspagen@maastrichtuniversity.nl
N. von Tunzelmann
SPRU, Freeman Centre, University of Sussex,
Falmer, Brighton BN1 9QE, UK
e-mail: g.n.von-tunzelmann@sussex.ac.uk
123
Cliometrica (2011) 5:291–321
DOI 10.1007/s11698-011-0063-6
1 Introduction
The steam engine has still a central position in the economic history of the British
industrial revolution. Today, it is generally recognized that traditional accounts of
the industrialization process such as those of Rostow (1960) and Landes (1969)
tended to conflate the economic significance of the steam engine with its early
diffusion. In fact, the available shreds of evidence on the growth of steam power in
the British economy in combination with data on the cost effectiveness of early
steam engines indicate that steam power gave a only modest contribution to
aggregate productivity growth until at least the 1830s (Von Tunzelmann 1978,
Crafts 2004a, b).
However, it is important to stress that these revisionist accounts concern the
timing of the economic effects of the diffusion of steam power technology and do
not intend to question the fundamental role played by this technology for economic
growth over the long-run. Thus, the views of Cipolla (1962) and Wrigley (1988,
2004) which regard steam power as a critical technological breakthrough that
changed the energy budget of the British economy providing the opportunity for
tapping into inorganic stocks of fossil fuels (coal) and thereby reaching a steeper
growth trajectory (usually referred to as ‘‘modern economic growth’’) are not in
principle in contrast with the findings of Crafts and von Tunzelmann. Recent
developments in growth theory have actually pointed out a series of factors which
can explain why the impact of a general purpose technology such as the steam
engine on the rate of economic growth is going to be affected by long delays
(Lipsey et al. 2005; Bresnahan 2010).
This cursory summary suggests that the broad contours of the relationship
between the diffusion of steam power and economic growth have been probably
successfully outlined. However, this concerns only the aggregate dimensions of the
diffusion process. In fact, several contributions have actually argued that a proper
understanding of the processes of economic change occurring during the British
industrial revolution needs to be based on a regional perspective (Pollard 1981;
Langton 1984; Hudson 1989; Berg and Hudson 1992). These authors claim that
industries exhibiting fast rates of output growth and extensive technical and
organizational changes displayed a strong tendency towards regional concentra-
tion.1 From these considerations, it is clear that, when accounting for the diffusion
of a technology in this period, due attention must be paid to regional aspects.
Kanefsky (1979) and Kanefsky and Robey (1980) have assembled a compre-
hensive data-set on the adoption of steam power in Britain throughout the eighteenth
century. On the basis of these data, they have provided a quantitative descriptive
outline of the diffusion process (Kanefsky and Robey 1980). This paper serves a
twofold purpose. The first aim is to expand on Kanefsky and Robey by providing a
new quantitative characterization of the timing, the pace and the geographical extent
of steam engine diffusion during the eighteenth century adopting a framework of
1 This emphasis on the importance of geography is actually also somewhat implicit in the Crafts and
Harley (1992) position via the emphasis given specificities of the growth experience of the (Lancashire)
cotton industry.
292 A. Nuvolari et al.
123
inquiry based on the economics of technological diffusion. The second goal is to
assess the factors influencing the adoption of steam engine technology in different
locations. In particular, we want to test systematically the role played by the price of
coal, which the studies of von Tunzelmann (1978, pp. 47–92) and Kanefsky (1979)
have identified as the critical factor affecting steam engine usage. In this respect, it
is worth noting that both the studies of von Tunzelmann (1978) and Kanefsky
(1979) were based on estimates of the cost effectiveness of ‘‘representative’’
Newcomen and Watt engines at different level coal prices integrated by some
anecdotal evidence (e.g. von Tunzelmann 1978, pp. 76–78), but they did not
investigate systematically the existence of an actual correlation between coal prices
and the number of engines installed at regional level.2
The rest of the paper is organised as follows. In the next section we present a
brief overview of the development of the steam power technology in the course of
the eighteenth century. Clearly the aim of this section is to provide the necessary
background (from the history of technology point of veiw) to our diffusion study. In
Sect. 3, we provide a broad outline of the geographical diffusion patterns of
Newcomen and Watt engines. Section 4 examines the timing and pace of steam
engine diffusion at the level of individual counties. In Sect. 5, by estimating
‘‘adoption equations’’ of various types of steam engines by county, we assess the
relative role of a number of specific location factors. In the same section, we also
attempt to interpret the results of our econometric analysis against the background
of the existing historical accounts of the emergence of steam power technology.
Section 6 draws conclusions.
2 The development of the steam engine during the eighteenth century
In the late seventeenth century mining activities began to be severely hampered by
flooding problems. Following the scientific investigations of Torricelli and Pascal,
there were several attempts to use atmospheric pressure to lift water out of mines.
The Savery engine, clearly inspired by the scientific investigations of the time, can
be considered as the first successful effort in this direction. The engine was
developed in the period 1695–1702. In the Savery engine, steam was first admitted
and then condensed inside a ‘‘receiving’’ vessel by pouring cold water over its
outside. Following steam condensation, atmospheric pressure drove the water to be
pumped up into the vessel. The engine suffered from two major shortcomings,
which severely limited its practical utilization. The first defect was the restricted
height of operation: the suction lift could raise water only to a height of 20 feet
(about six metres). The second was the high fuel consumption due to the need to re-
create steam inside the vessel at each stroke. Undoubtedly, the historical importance
of the Savery engine lies more in showing the general potentialities of the use of
2 A study similar to the one carried out in this paper has been performed by Atack et al. (1980) for the
adoption and regional diffusion of steam power in the United States over the period 1776–1900. In a study
related to the present paper, Nuvolari and Verspagen (2009) examine the patterns of diffusion of the high
pressure engine in Britain in the period 1800–1850.
The early diffusion of the steam engine in Britain 293
123
steam power rather than in its practical applications, although a number of such
engines continued to be in actual use for several years.
The Newcomen engine, developed in the early 1710s, resolved the problem of
the limited height of operation. The engine consisted of a piston-cylinder
arrangement connected to one arm of a working beam. The opposite end of the
working beam was connected to the mine pump-rod. Steam was admitted from the
boiler into the cylinder by means of a valve. Then a cold jet of water was sprayed
into the cylinder, condensing the steam. This created a partial vacuum inside the
cylinder, so that the piston was pushed down by atmospheric pressure3 (the top of
the cylinder was open), lifting the pump-rod at the other end of the beam. The use of
the cylinder-piston arrangement together with the beam made possible the use of the
engine for effective mine drainage, as pump-rods could easily be extended to reach
the necessary depth. Furthermore, the Newcomen engine was robust, highly reliable
and based on a fairly simple working principle. Given these merits, it is not
surprising that Newcomen engines soon came into widespread use in mining
activities. However, the Newcomen engine had two main technical shortcomings.
As with the Savery engine, one deficiency was the high fuel consumption due to the
need for cooling and heating the cylinder at each stroke. The second limitation was
the irregularity of its movement, which prevented the use of this kind of engine for
directly delivering rotary motion.4 Savery and Newcomen formed a partnership to
exploit the patent rights of their inventions (Savery had been granted a patent for his
invention in 1699). The patent expired in 1733.
The problem of the high fuel consumption of the Newcomen engine was
successfully tackled by James Watt in the late 1760s. In the Watt engine
condensation was carried out in a separate vessel and not in the cylinder, so there
was no need to re-heat the cylinder at each stroke. The Watt engine, like the
Newcomen engine, consisted of a piston-cylinder arrangement connected with a
working beam, but the piston was pushed down by the action of steam and not by
atmospheric pressure (the cylinder had a closed top). After having pushed down the
piston, the steam was admitted by means of a system of valves into a separate vessel
where it was condensed. This allowed for a much higher fuel economy compared to
the Newcomen engine.
In the second half of the eighteenth century, there were also a number of attempts
to introduce modifications to the Newcomen engine so that it could deliver a steady
rotary motion. The most convenient solution was patented in 1780 by James
Pickard. It involved the combined use of the crank and a flywheel (Hills 1989,
p. 60). At more or less the same period, Watt, at the insistence of his business
partner Matthew Boulton, was also working on the transformation of reciprocating
into rotary motion. Pre-empted by Pickard in the use of the crank, Watt was forced
to contrive an alternative mechanical device, the ‘‘sun and planet’’ gear. However,
after the expiration of Pickard’s patent, in 1794, Boulton and Watt resorted to the
3 For this reason, Newcomen and Savery engines were also commonly termed ‘‘atmospheric’’ engines.
4 A number of Newcomen engines were successfully used to raise water over a water wheel which, in
turn, delivered rotary motion for factory machinery. This type of engine was usually called a ‘‘returning
engine’’. One major limitation of this engine was that the inefficiency of the water-wheel was combined
with the inefficiency of the engine. See Hills (1989, p. 49).
294 A. Nuvolari et al.
123
use of the simpler and more effective crank (von Tunzelmann 1978, p. 20). The
conversion of reciprocating into rotary motion was also facilitated by the
development of the double-acting engine, another invention by Watt, which was
patented in 1782. In the double-acting engine steam is alternatively admitted into
the cylinder on both sides of the piston. This resulted in a more powerful action, but
also in a much more uniform movement of the piston, making the Boulton and Watt
double-acting design the state-of-the-art for applications requiring rotary motion.
Accordingly, at the end of the eighteenth century, Watt engines probably enjoyed
some technical advantage in applications requiring the delivery of a steady rotary
motion, such as cotton spinning. From the 1780s, Newcomen engines had also
begun to be used to drive textile machinery, but the motion they delivered was
rather unsteady (Hills 1970, pp. 141–143). Some ingenious technical solutions that
could mitigate this problem were introduced in the early 1790s by Francis
Thompson and Bateman and Sherrat for Newcomen engines installed in cotton mills
in Lancashire and Nottinghamshire (Hills 1970, pp. 147–148).
Finally, in the second half of the 1790s, Richard Trevithick developed the first
high-pressure engine (Watt engines used steam at a little more than atmospheric
pressure). This type of engine did not use the separate condenser, but discharged
exhaust steam directly into the atmosphere. For this reason, they were called
‘‘puffers’’. The main advantage of this type of engines was their compactness and
their cheaper cost of installation due to elimination of the condenser, the air pump
and the beam (von Tunzelmann 1978, p. 23). The nineteenth-century development
of steam power technology was to be increasingly characterized by the use of higher
and higher steam pressures, though usually in combination with condensing.
3 Spatial diffusion patterns in early steam power technology
Kanefsky and Robey (1980) have compiled a survey of all the steam engines erected
in Great Britain in the course of the eighteenth century.5 For each (known) steam
engine erected during the period 1700–1800, Kanefsky and Robey recorded the year
of construction, the type or design of the engine (i.e. Newcomen, Watt, Hornblower,
etc.), the county, and the sector of application.6 It is worth remarking that this
dataset intends to cover engine construction and not engine utilization. This means
that besides the year of erection there is no other information on the time period
over which the engine was actually used, and there is no information on the date at
which the engine was scrapped or replaced.
As the authors would admit, the data collected by Kanefsky and Robey are
probably affected by some biases in both upward and downward directions. The
principal source of overestimation is the double counting of engines that were
moved from one place to another, whereas underestimation is mainly due to small
engines that have left no trace in the records. Notwithstanding these problems
(which might result in some revisions in the future), the survey constitutes the most
5 See Kanefsky (1979) for a detailed account of the construction of the database.
6 Other information available for some of the engines is the maker, the cylinder size and the horsepower.
The early diffusion of the steam engine in Britain 295
123
accurate attempt to trace the growth of steam power in Britain over the eighteenth
century. In this work, we employ an up-to-date version of this dataset compiled by
Kanefsky.7
On the basis of the historical outline presented in the previous chapter, the
development of steam power technology in the eighteenth century can be divided
rather naturally into three distinct ‘‘epochs’’. The first epoch (1700–1733) goes from
the invention of the Savery engine to the expiration of the Savery-Newcomen
patent. This phase represents the early introduction of the new technology. The
second epoch covers the period 1734–1774. The final phase goes from 1775 (the
year of the first successful erection of a Watt engine) to 1800 (the year in which
Watt’s patent for the separate condenser expired).
For analysing the geographical patterns of steam usage in the eighteenth century,
the county seems indeed the appropriate unit of analysis. Historians advocating the
adoption of a regional perspective have actually used counties to identify the regional
economic systems (Pollard 1981; Hudson 1989). Further, Langton has actually
argued that the origins of economic regionalism in England are actually based on the
growing autonomy of a ‘‘county society’’ during the seventeenth century, so that by
the eighteenth century counties represented relatively coherent geographical units
characterized by well defined and specific economic concerns and also cemented by
well defined common social identities and cultures (Langton 1984). Other studies
focussed on specific regional dimensions of the industrialization process such as the
dynamics of wages (Hunt 1986) have used county level data.
The maps presented in Fig. 1 provide a preliminary ‘‘impressionistic’’ view of
the geographical (county) distribution of the engines erected in these three periods.
Darker (lighter) areas indicate a higher (lower) number of engines. White areas
indicate that no engines were erected in that particular county. In addition, map 5
represents the geographical distribution of water-wheels (the ‘‘predominant’’ power
technology of the period) and map 6 illustrates the prevailing level of coal prices in
the various counties in (circa) 1800 (again, darker areas indicate higher prices,
lighter areas represent lower prices and in this case white areas correspond to
missing values).8
Looking at the maps, the spread of steam power technology appears to have been,
from the very outset, remarkably wide.9 There is some evidence that indicates that is
7 The results of a preliminary analysis of diffusion trends in the updated version of Kanefsky data-set
have been reported in Nuvolari et al. (2006). The list originally compiled by Kanefsky and Robey
contained a total of 2,191 steam engines, the new updated dataset contains 2,279 engines. The updated
version of the list has been kindly provided to us by John Kanefsky. Concerning Watt engines, the
updated list by Kanefsky contains 479 engines. Tann (1988) on the basis of a careful examination of the
Boulton and Watt papers considers this total too high. Her estimation of the engines constructed by
Boulton and Watt by 1800 is 449. In this work, mainly for sake of convenience, we have utilised
Kanefsky’s list without attempting corrections.
8 The source for the number of water wheels is Kanefsky (1979, pp. 215–216) and for coal prices von
Tunzelmann (1978, p. 148).
9 Note that maps 1, 2 and 3 show the distribution of Newcomen and Savery engines considered together.
As a consequence, a more precise definition would be ‘‘atmospheric engines’’. Given the relatively small
number of Savery engines installed, we have decided to ignore the distinction and maintain the most
common usage of Newcomen engines.
296 A. Nuvolari et al.
123
highly likely that the first Newcomen engine was erected in Cornwall at the Wheal
Vor tin mine in 1710. However, because of the high price of coal, Cornwall did not
represent the most fertile soil for the diffusion of the new technology. The erection
of the Wheal Vor engine remained a sporadic event and the introduction of
Newcomen engines in Cornish mines actually took place only from the 1720s (Rolt
and Allen 1997, p. 45).
Coal mining areas represented of course a much more receptive environment for
the new technology, since there coal would be relatively cheap. The Midlands
Fig. 1 Geographical diffusion of steam technology, 1700–1800
The early diffusion of the steam engine in Britain 297
123
coalfields (Stafford and Warwickshire) were the first location where Newcomen
engines could take firm root. The commercialisation of the engine was at first
controlled by the Newcomen–Savery partnership. As mentioned in the previous
chapter, after Savery’s death in 1715, a syndicate for the exploitation of the patent
rights, the ‘‘Committee of Proprietors of the Invention for Raising Water by Fire’’
was constituted. The Committee, under the direction of its secretary John Meres,
promoted rather successfully the use of the engines for drainage in various mining
areas by means of a network of agents and licensees.10 Apart from the Midlands, as
the map of Fig. 1 indicates, by 1733, Newcomen engines, had been adopted in some
numbers in Cornwall and in the coalfields in the North East (Northumberland and
Durham).
Overall, during the monopoly of the ‘‘Proprietors’’ about one hundred Newcomen
engines were constructed. As Smith (1978, p. 12) has aptly remarked, for the time,
this must be considered ‘‘by any standards a colossal business achievement’’. On the
other hand, it should also be noted that historians (see for example, Flinn 1984,
p.117) have generally contended that the high level of royalties claimed by the
‘‘Proprietors’’ (up to £350 a year) hampered the diffusion process in this initial
phase.11 Be this as it may, one has to acknowledge that, under the ‘‘Proprietors’’, a
group of skilled engine-builders emerged. As we have mentioned in the previous
chapter, one of the main merits of Newcomen’s invention was its relative easiness
of construction and maintenance. Nonetheless, in this initial phase, the engine still
represented a rather sophisticated piece of equipment and its erection probably
called for more than ordinary engineering skills. Thus, the formation and
consolidation of this base of engine-building skills presumably represented a
critical factor for the successful introduction of steam power in various locations.
Among these engineers we may mention Henry Beighton, who worked for the
Parrot-Sparrow partnership and compiled a table containing some rules of thumb for
the proportions of the various components of the engine; Joseph Hornblower, who
supervised the erection of various engines first in the Midlands and then in
Cornwall12; Samuel Calley, the son of John Calley (the partner of Thomas
Newcomen in the invention of the engine); and Marten Triewald, a Swedish
engineer who installed various Newcomen engines in the North East and who would
erect a (not very successful) Newcomen engine in Sweden at the Dannemora mine.
In the period 1734–1774 Newcomen engines continued to be built in mining
areas. However, as we can we see from map 2, in this phase, steam power also
penetrated new locations. This wider spread of the engine was mainly due to its
10 The most active licensee of the ‘‘Proprietors’’ was the partnership formed by Stonier Parrot and
George Sparrow who were engaged in the erection of more than fifteen Newcomen engines. According to
Flinn (1984, p. 120), the high number of engines erected in Warwick and Stafford (far in excess of the
two counties’ share in British coal production) is to be accounted for by the fact this was the ‘‘home
stronghold’’ of the Parrot–Sparrow partnership. For an account of the activities of Stonier Parrot, see
Rowlands (1969).
11 Kanefsky’s data provide some quantitative support for this view. From 1710 to 1733, 95 Savery–
Newcomen engines were constructed. This is approximately equal to 4 engines erected per year. In the
period 1734–1774, instead, 442 engines were built, corresponding to 11 engines per year.
12 Joseph Hornblower would decide to settle definitely in Cornwall. He was the grandfather of Jonathan,
the inventor of the compound engine.
298 A. Nuvolari et al.
123
adoption by the iron sector (Shropshire) where it was used to assist water wheels in
blowing coke blast furnaces during drought periods (Hyde 1977, pp. 69–75).
Newcomen engines also began to be constructed in some numbers in Scotland in the
counties of the Clyde Valley.13
In this second phase, the ‘‘Proprietors’’ had completely ceased to control the
market and Newcomen engines were typically erected by local craftsmen, leaving
the cylinder, the cylinder bottom and a small number of other critical components to
be manufactured by ‘‘specialist’’ firms and then shipped to the location of the
engine. In this respect, it is worth noting that, up to the early 1780s, in Britain there
existed only four ironworks that could supply cast iron cylinders for steam engines
namely Coalbrookdale and New Willey (in Shropshire), Bersham (in Denbigh) and
Carron (Stirling).
The period 1775–1800 is characterized by the competition between Watt and
Newcomen engines. In this phase, typically textile counties such as Lancashire and
Renfrew (cotton) and West Riding (wool) began to resort to some use of steam to
power machinery. The main difference in the spread of the two types of engines is
that Watt engines appeared capable of achieving some penetration (although in low
numbers) in the counties of the South East, an area which appears, by and large, to
exclude Newcomen engines.
Table 1 reports Moran I statistics for the three periods we are considering. Moran
I statistic measures whether a variable displays a tendency to be systematically
clustered in space, or, on the contrary, it is randomly spread. Higher values of
Moran I statistic indicate a stronger degree of spatial autocorrelation. In other
words, higher values of the statistic mean that counties with relatively high number
of engines tend to be neighbouring (see ‘‘Appendix 1’’, for more details on the
calculation of Moran I statistic).
Table 1 shows that Moran I statistic is higher for Newcomen engines than for
Watt engines. Notably, in the case of Newcomen engines the coefficient appears to
be significantly different from zero both when the original variable is assumed to be
characterized by a normal distribution and when it is supposed to be generated by an
unspecified one (randomized).
Table 1 Spatial autocorrelation between engines
Type of
engine
Period Number of
engines
Moran I
statistic
Significance
(normal)
Significance
(randomized)
Newcomen 1700–1733 97 0.167 ** ***
Newcomen 1734–1774 442 0.124 * **
Newcomen 1775–1800 616 0.192 *** ***
Boulton & Watt 1775–1800 479 0.074
*, **, *** indicate significance levels of 10, 5 and 1% respectively
13 For an account of these cases of early installation of Newcomen engines in Scotland, see Hills (2002,
p. 297).
The early diffusion of the steam engine in Britain 299
123
On the contrary, the Moran I statistic for Boulton and Watt engines does not turn
out to be significant. This seems to indicate that the adoption of Boulton and Watt
engines was less susceptible of being conditioned by specific local conditions. This
finding may be accounted for by two possible sets of factors acting respectively on
the demand and the supply side. On the demand side, given its superior fuel
efficiency, it is likely that the adoption of Watt engines was less conditioned by the
proximity to cheap coal (this is indeed consistent with the penetration of the Watt
engine in the South East of England).
Concerning the possible existence of spatial constraints from the supply side, it is
worth noting that apart, from the early period of the ‘‘Proprietors’’, the installation of
Newcomen engines was typically in the hands of local millwrights and for this reason,
the geographical adoption of the engine could have been limited to areas endowed
with the necessary amount of engineering skills. On the contrary, as we shall see,
Boulton and Watt instead adopted immediately a much wider horizon in their
marketing of steam engines, aiming to serve the entire national market for power.
4 The diffusion paths at the county level
The literature on the diffusion of innovations has generally found that the diffusion
process follows an S-shaped or sigmoid pattern. The diffusion process takes off
rather slowly, then, after a while, it accelerates, and finally it slows down until a
certain saturation level is reached (for two insightful overviews of the literature on
the diffusion of inventions, see Lissoni and Metcalfe (1994) and Stoneman (2002)).
Also in our case, the dynamics of the cumulative number of engines installed seems
to follow, in most counties, an S-shaped profile. Following the pioneering
contribution of Griliches (1957), it has been common to estimate a simple
symmetric logistic growth equation such as (1) in order to provide a characterization
of the diffusion process14:
Nt ¼ K
1 þ eðaðtbÞÞ ð1Þ
In Eq. 1, t represents time (expressed in years), Nt is the number of steam engines
installed at time t, K is the saturation level (the number of steam engines that will be
installed at the end of the diffusion process), a is a parameter which determines the
slope of the curve and the can be understood as a measure of the speed of the diffusion
process (the higher the value, the faster the diffusion process), the parameter b,
instead, defines the position of the curve (b indicates when the curve reaches the value
K/2, that is to say the midpoint of the diffusion process). Some more recent
contributions have however found that in some circumstances non symmetric
specifications such as the Gompertz growth curve provide a better fit.15
14 The symmetric logistic curve has been employed by Atack et al. (1980) for providing a
characterization of the diffusion process of steam power at regional level in the American case.
15 See Dixon (1980) for an application to the case of hybrid corn studied by Griliches and Geroski (2000)
for a more general discussion.
300 A. Nuvolari et al.
123
In this perspective, the analysis of data on innovation diffusion using a
generalized version of the simple logistic growth equation originally suggested by
Richards (1959; see also Birch (1999) for a thorough discussion) in the study of
growth processes in the field of botany seems particularly promising. The Richards
equation is given by:
Nt ¼ K
1 þ T  eðaðtbÞÞð Þð1=TÞ
ð2Þ
In Eq. 2 the definition of the variables and parameters is the same of Eq. 1. In
comparison to Eqs. 1, 2 contains a fourth shape-parameter, T. It can be shown
that the Richards equation encompasses the logistic and the Gompertz as special
cases: when the parameter T = 1 we are in the case of the simple logistic
equation, when T ? 0 the Richards equation tends towards the Gompertz growth
curve. The chief advantage of the Richards equation is clearly that by containing
the additional shape-parameter T, it can be used to characterize a wide variety of
sigmoid patterns with different positions of the inflection point. In general, if
T \ 1 the inflection point of the curve will be located when Nt \ K/2, instead
if T [ 1 the inflection point will be situated in correspondence of a value of
Nt [ K/2.
Using non linear least squares, we have estimated both the simple logistic
equation (‘‘symmetric’’) and the Richards equation (‘‘generalized’’) for each county
and adopted as preferred model the one that provided a better fit of the data (we
have done this exercise for counties with at least 10 engines installed in the period
1700–1800). In order to characterize the relative speed of the diffusion process in
each county we have calculated the parameter Dt, which is the number of years
needed to grow from the 10 to the 90% of the estimated saturation level K (Grubler
1990, pp. 14–15).16 The results are reported in Table 2. The full estimates are
instead reported in Table 5 in ‘‘Appendix 2’’. The estimated diffusion paths for
Newcomen and Watt engines are represented in Figs. 2 and 3 together with the
cumulative number of engines (represented by the dots).
In the case of Newcomen engines the generalized specification is preferred in 11
counties whereas the standard symmetric logistic in 10 counties. In the case of
Watt engines, instead, the generalized specification is preferred in 2 counties
whereas the standard symmetric logistic in 9. Note that in the case of Newcomen
engines, for ten counties the estimates of the parameter T are greater than 1. This
means that the S curves display an asymmetric growth pattern where the point of
inflection is situated to the right of the point Nt = K/2. This finding may perhaps
be interpreted as an effect of the competition of Watt engines in the last 25 years
of our time window causing a progressive slowing down of the rate of growth of
Newcomen engines.
Figure 2 and Table 2 reveal some other interesting aspects of the spread of
Newcomen engines. There is a group of ‘‘pioneer’’ counties characterized by
relatively fast diffusion rates (Dt \ 40). These locations are Cornwall where steam
16 It can be shown that in the case of the logistic Dt ¼ ln 81b and in the case of the Richards equation
Dt ¼ lnð10T1Þ lnðð1=0:9ÞT1Þb .
The early diffusion of the steam engine in Britain 301
123
T
a
b
le
2
R
at
es
o
f
d
if
fu
si
o
n
o
f
N
ew
co
m
en
an
d
B
o
u
lt
o
n
&
W
at
t
en
g
in
es
,
1
7
0
0
–
1
8
0
0
C
o
u
n
ty
N
ew
co
m
en
en
g
in
es
B
o
u
lt
o
n
&
W
at
t
en
g
in
es
N
u
m
b
er
o
f
en
g
in
es
F
ir
st
in
st
al
le
d
M
id
p
o
in
t
D
t
P
re
fe
rr
ed
M
o
d
el
N
u
m
b
er
o
f
en
g
in
es
F
ir
st
in
st
al
le
d
M
id
p
o
in
t
D
t
P
re
fe
rr
ed
M
o
d
el
C
h
es
h
ir
e
1
7
1
7
7
8
1
7
9
5
2
0
S
y
m
m
et
ri
c
C
o
rn
w
al
l
7
5
1
7
1
0
1
7
6
7
4
2
G
en
er
al
iz
ed
5
6
1
7
7
7
1
7
8
1
1
5
G
en
er
al
iz
ed
C
u
m
b
er
la
n
d
2
3
1
7
1
7
1
8
7
8
1
1
3
S
y
m
m
et
ri
c
D
er
b
y
6
2
1
7
1
7
1
7
9
1
8
1
S
y
m
m
et
ri
c
D
u
rh
am
1
0
3
1
7
1
7
1
7
7
1
7
5
S
y
m
m
et
ri
c
1
8
1
7
9
1
1
7
9
6
5
S
y
m
m
et
ri
c
G
lo
u
ce
st
er
4
9
1
7
3
5
1
7
7
0
5
3
S
y
m
m
et
ri
c
L
an
ca
sh
ir
e
8
5
1
7
1
9
1
8
2
7
3
8
G
en
er
al
iz
ed
7
4
1
7
7
7
1
8
1
0
1
1
G
en
er
al
iz
ed
L
ei
ce
st
er
1
0
1
7
2
4
1
7
7
1
7
8
S
y
m
m
et
ri
c
L
o
n
d
o
n
4
4
1
6
9
8
1
8
5
5
7
9
G
en
er
al
iz
ed
7
7
1
7
7
6
1
7
9
4
2
4
S
y
m
m
et
ri
c
N
o
rt
h
u
m
b
er
la
n
d
1
6
3
1
7
1
8
1
7
7
3
7
0
S
y
m
m
et
ri
c
2
0
1
7
7
8
1
8
0
2
1
8
S
y
m
m
et
ri
c
N
o
tt
in
g
h
am
1
6
1
7
2
8
1
8
4
8
7
0
G
en
er
al
iz
ed
1
8
1
7
8
6
1
7
8
9
7
S
y
m
m
et
ri
c
S
h
ro
p
sh
ir
e
7
4
1
7
1
5
1
8
1
8
1
1
4
S
y
m
m
et
ri
c
4
4
1
7
7
6
1
7
8
6
1
7
S
y
m
m
et
ri
c
S
ta
ff
o
rd
5
9
1
7
0
6
1
7
9
5
7
2
G
en
er
al
iz
ed
3
8
1
7
7
5
1
7
8
8
2
4
S
y
m
m
et
ri
c
W
ar
w
ic
k
3
9
1
7
1
4
1
7
6
0
1
3
0
S
y
m
m
et
ri
c
1
1
1
7
7
7
1
8
0
8
3
8
S
y
m
m
et
ri
c
W
o
rc
es
te
r
1
3
1
7
2
5
1
8
3
3
1
0
3
G
en
er
al
iz
ed
W
es
t
R
id
in
g
1
0
0
1
7
1
5
1
8
1
6
4
4
G
en
er
al
iz
ed
2
2
1
7
8
2
1
7
9
9
2
0
S
y
m
m
et
ri
c
F
li
n
t
1
9
1
7
1
5
1
7
3
2
6
5
G
en
er
al
iz
ed
G
la
m
o
rg
an
1
3
1
7
1
7
1
7
6
3
3
8
S
y
m
m
et
ri
c
A
y
r
3
2
1
7
2
0
1
7
9
5
4
3
G
en
er
al
iz
ed
F
if
e
2
1
1
7
6
4
1
8
2
4
3
9
G
en
er
al
iz
ed
L
an
ar
k
2
6
1
7
6
0
1
7
9
2
3
6
S
y
m
m
et
ri
c
S
ti
rl
in
g
1
8
1
7
6
0
1
8
1
8
4
5
G
en
er
al
iz
ed
A
v
er
ag
e
4
9
1
7
2
3
1
8
0
0
6
8
3
6
1
7
7
9
1
7
9
5
1
8
D
t
is
th
e
n
u
m
b
er
o
f
y
ea
rs
n
ec
es
sa
ry
fo
r
m
o
v
in
g
fr
o
m
1
0
to
9
0
%
o
f
th
e
es
ti
m
at
ed
sa
tu
ra
ti
o
n
le
v
el
302 A. Nuvolari et al.
123
engines were employed in copper and tin mines, some typical ‘‘textile’’ counties like
Lancashire (cotton) and West Riding and Gloucester (wool) and the Scottish
counties (Ayr, Lanark, Fife and Stirling). It is worth noting that in Scotland the
Fig. 2 Estimated diffusion paths for Newcomen engines
The early diffusion of the steam engine in Britain 303
123
diffusion begins only in the second half of the eighteenth century (around 1760).
Presumably, the establishment of the Carron ironworks (which made use of the
cylinder boring machine designed by John Smeaton) in Stirling in 1760 spurred the
Fig. 2 continued
304 A. Nuvolari et al.
123
rapid adoption of steam power in several Scottish counties from the early 1760s.17
Coal mining areas of the Midlands (Derby) and of the North East (Northumberland
and Durham) together with the London and Nottingham, Stafford and Leicester are
characterized by intermediate rates of diffusion (60 \ Dt \ 100). Finally there is a
group of ‘‘laggard’’ counties with relatively slow diffusion rates (Dt [ 100):
Warwick, Shropshire [where from 1743 Newcomen engines where used in
ironworks (Trinder 1973)], Cumberland and Worcester.
Fig. 2 continued
17 In the late 1760s and 1770s, Watt himself was involved in the installation of several Newcomen
engines in Scotland. The erection of these engines provided Watt, who was until then acquainted only
with experimental models, with a good deal of practical experience with the problems related with the
installation and operation of full scale engines (Hills 2002, p. 358).
The early diffusion of the steam engine in Britain 305
123
Table 2 also shows that, in general, Boulton and Watt engines were characterized
by a faster diffusion rate. The average rate of diffusion (Dt) for Newcomen engines
is equal to 68 years, whereas for Watt engines it is equal to 18 years.
Fig. 3 Estimated diffusion paths for Watt engines
306 A. Nuvolari et al.
123
As in the case of Newcomen engines, the adoption of the Watt engine in various
locations also appears to be characterized by a sequential order. Also in the case of
Watt engines, we can identify a group of ‘‘pioneer’’ counties such as Cornwall,
Shropshire, Northumberland, Durham and Lancashire where the diffusion process is
particularly fast (Dt \ 20). We have regions with intermediate rates of diffusion such
as Cheshire and West Riding (Dt = 20). Finally, we have ‘‘laggard’’ counties with
relatively slow diffusion rates such as London, Stafford and Warwick (Dt [ 24).
This general exploration of the patterns of diffusion confirms that steam engine
technology by the end of the eighteenth century had already become a source of
power capable of being used in a wide variety of production processes and in
different local contexts. Of course, this exercise is simply meant to provide a broad
characterization of the diffusion process in different locations. As noted by Dosi:
…[T]he ‘logistic curves’ approaches to technological diffusion…show the
same descriptive usefulness as well the same limitations of the epidemic
curves (or, for that matter, probability models) to which they are formally
similar: they show the pattern of diffusion of, say cholera, and they can also
relate it to some broad environmental factors, such as the conditions of
hygiene of a town, the reproduction time of bacteria, etc. but they cannot
explain why some people get it and other do not, which relates to the
immunological mechanisms of human bodies, the precise ways bacteria are
transmitted, and so on (Dosi 1984, p. 286, italics in the text).
Fig. 3 continued
The early diffusion of the steam engine in Britain 307
123
In other words, our reconstruction of the patterns of diffusion needs to be integrated
by further research on the ‘‘microbiology’’ of the diffusion process.
5 An econometric model of engine adoption for the period 1775–1800
In order to shed some additional light on the factors driving the spread of steam
power technology in this section we estimate ‘‘adoption’’ equations for eighteenth
century steam engines using a cross section of counties. We focus on the late
eighteenth century (1775–1800) and compare systematically the factors affecting
the installation of Newcomen versus Watt engines. Clearly, the aim is to check
whether there were noteworthy differences in the factors driving the diffusion
process of the two types of engines. Our dependent variable is the number of steam
engines (Newcomen or Watt) erected in each county in the period 1775–1800. In
both cases, we have a count variable that is skewed, with a non-negligible number of
counties having no (i.e., zero) engines. Accordingly, we will make use of negative
binomial regressions for estimating the two models (Greene 2000, pp. 880–893; for
a thorough treatment of the regression analysis of count data, see also Cameron and
Trivedi 1998).
The explanatory variables are:
(i) the price of coal prevailing in the county;
(ii) a dummy indicating the level of coal prices in a dichotomous way (i.e. low/
high, with low being approximately less than 14 s.). This characterization of
the price of coal variable permits us to use in the estimation of the regression
equation all the counties (84) and not just the 41 for which coal prices are
directly available. The dummy variable has been constructed considering the
studies of the coal mining industry of Flinn (1984), von Tunzelmann (1986)
and Turnbull (1987);
(iii) the number of water-wheels, which can be considered as a proxy for the
demand for power (note that in some applications such as ironworks and
textiles, steam engines were initially used the operation of water-wheels
during drought periods);
(iv) the number of patents in steam technology taken by residents in the county
over the period (1698–1801). This variable should capture, admittedly in a
rough way, the depth of steam engineering skills existing in the county in
question18;
(v) the number of blast furnaces in operation existing in the county c. 1800;
(vi) the number of cotton mills existing in the county c. 1800;
(vii) the number of wool mills existing in the county c. 1800;
(viii) for the counties with collieries, the output of coal (in 000s of tons) in 1800;
(ix) a dummy variable indicating the industrial counties: these are the counties
identified by Wrigley (2006, p. 19) as those where, in the second half of
the eighteenth century, employment in manufacturing was growing fastest.
18 In case of patents granted to multiple patentees with residence in different counties, each county was
credited with one patent.
308 A. Nuvolari et al.
123
By 1831, all these counties had a share of agricultural male employment of
less than 20%.
(x) the population of the county in 1801 in (000s).
A complete description of the sources and of the construction of the variables
used is given in ‘‘Appendix 3’’. Table 6 in ‘‘Appendix 3’’ reports the descriptive
statistics.
Admittedly, our set of explanatory variables is far from covering all the
potential factors affecting the diffusion of steam technology in the period in
question. Coal prices reflect the cost of a unit of power for the adopter of a steam
engine. However the coefficient can also reflect the use of the steam engine in
coal mines (as in coal mining areas coal was cheap). We try to control for this
latter effect by including in the regression also the coal output mined in counties
with collieries. Similarly, the number of water wheels is a proxy for the overall
demand of power existing in the county but, at the same time, the variable may
also capture some ‘‘substitution’’ or ‘‘complementarity’’ effects between steam and
water power.19
The sectoral variables (number of blast furnaces, number of cotton mills,
number of woollen mills, output of coal), are used as proxies for the size of
different branches of economic activities in various counties and control for the
different (steam) power requirements of application sectors. They provide a
measure of the size of industries (ironworks, textiles and coal mining) that were
among the most intensive users of steam power and are included in order to assess
the influence of the production structure of the county on the patterns of engine
adoption. Note that our coverage of application sectors cannot by any means
considered as exhaustive. Lack of suitable data has prevented us from estimating
for a sufficient number of counties the size of other sectors which were very
intensive users of steam power, such as breweries and waterworks and canals. In
order to address this issue, in some specifications we have included the dummy
‘‘industry’’ taken from Wrigley (2006) indicating the counties with the fastest
growth in manufacturing employment at the end of the eighteenth century. The
variable population is also introduced as an additional control for the different
sizes of the counties.
The variable ‘‘patents in steam technology’’ is aimed at capturing the ‘‘depth’’ of
steam engineering skills existing in the county in question. Of course this is a very
imperfect proxy. As we have already mentioned, the high rates of diffusion for Watt
engines estimated in Table 2 were plausibly not only determined by the superior fuel
efficiency of the Watt engines, but also by the effectiveness of Boulton and Watt’s
organisation of steam engine production and marketing techniques. Since the very
outset, Boulton and Watt wanted to establish themselves as a leading ‘‘national’’
19 One would expect that abundance of cheap water power in one county had a dilatory effect on steam
engine diffusion. However, in many areas steam engines were used in combination of water wheels. In
addition, a county characterized by intensive use of water power was likely to be endowed with a strong
base of ‘‘millwrighting’’ skills that could have exerted a beneficial effect on the diffusion of steam power
technology.
The early diffusion of the steam engine in Britain 309
123
producer of steam engines.20 Instead, the construction of Newcomen engines was
mainly undertaken by local manufactures with rather narrower and less ambitious
business horizons.21 In this respect, Roll (1930) and Dickinson (1936) stressed the
fundamental role played by Boulton’s entrepreneurial and marketing abilities for the
success of the partnership.22 Boulton’s efforts ensured that Watt engines were
quickly adopted in a wide range of industrial applications, which before had not
made much use of steam power (breweries, textiles, etc.). For example, the erection
of the famous Albion Mills in London is frequently pointed out as an example of a
successful marketing strategy which succeeded in triggering the interest in steam
power of many industrialists (in particular, breweries) in the London area.23 Another
initiative of Boulton and Watt aimed at broadening the use of steam technology was
the publication of small technical booklets (of course only reserved for their
customers) providing detailed descriptions of the procedures for erecting and
operating their engines. In this way, ‘‘distant’’ customers could hopefully cope with
minor technical difficulties without the assistance of Boulton and Watt’s men.
Furthermore, Boulton and Watt successfully established standard units of
measure for both the fuel efficiency (duty) and the power (horsepower) of steam
engines. Note that the establishment of a standardized unit of power was an event
20 In a famous letter to Watt (February 7, 1769), Boulton declining the offer of Watt and Roebuck (the
first partner of Watt) of becoming the licensee of the Watt engine in three counties, wrote : ‘‘…I was
excited by two motives to offer you my assistance which were love for you and love of a money-getting
ingenious project. I presumed that your engine would require money, very accurate workmanship and
extensive correspondence to make it turn to best advantage and that the best means of keeping up the
reputation and doing the invention justice would be to keep the executive part out of the hands of the
multitude of empirical engineers, who from ignorance, want of experience and want of necessary
convenience would be very liable to produce bad and inaccurate workmanship; all of which would affect
the reputation of the invention. To remedy which and produce the most profit, my idea was to settle a
manufactory near to my own by the side of our canal where I would erect all the conveniences necessary
for the completion of engines and from which manufactory we would serve all the world with engines of
all sizes. By these means and your assistance we could engage and instruct some excellent workmen (with
more excellent tools that would be worth any man’s while to procure for one single engine) could execute
the invention 20 per cent cheaper than it would be otherwise executed, and with a great difference of
accuracy as there is between the blacksmith and the mathematical instrument maker. It would not be
worth my while to make for three counties only, but I find it very well worth to make for all the world’’
(quoted in Dickinson and Jenkins 1927, pp. 30–31, italics added).
21 For an account of the activities of local producers of atmospheric engines in Lancashire in the second
half of the eighteenth century, see Musson and Robinson (1969 pp. 393–426).
22 In his Memoir of Matthew Boulton written in 1809, Watt stressed the role played by Boulton’s
entrepreneurial abilities (and by his extensive network of acquaintances) for the successful development
of the engine partnership: ‘‘Boulton…possessed in a high degree the faculty of rendering any new
invention of his own or others useful to the publick, by organizing and arranging the processes by which it
could be carried on, as well as promoting the sale by his own exertions and by his numerous friends and
correspondents’’ (cited in Dickinson 1936, pp. 195–196).
23 The engines constructed for the Albion Mills were among the first rotary double acting engines
constructed by Boulton and Watt. The choice of a plant of the almost unprecedented size of the Albion
Mills was meant to attract the maximum of attention towards the new engine. From a strictly economic
point of view the undertaking was not successful. However, according to many contemporaries, following
the purely ‘‘mechanical’’ success of the mill, double-acting rotary engines were adopted in a variety of
industrial mills where direct rotary motion was needed (Westworth 1933). The engine erected at the
Albion Mill also convinced some textile manufacturers in the North to install Boulton and Watt engines
for powering their mills, see Hills (1970, p. 156).
310 A. Nuvolari et al.
123
not only of technical, but especially of economic significance (perhaps one of the
main determinants of the successful adoption of the engine in various manufacturing
applications). The horsepower unit permitted industrialists to have a rather reliable
assessment of their power requirements and it also permitted a rough, but rather
effective, cost-benefit analysis of the adoption of various power sources. Rules of
thumb soon came into common usage for expressing the power requirements of a
number of industrial processes [e.g. in cotton spinning 1 horsepower was typically
supposed to drive 100 spindles (Chapman 1971, p. 3)].
From these considerations it is clear that our econometric exercise can hope to
provide just a partial appraisal of the determinants of the usage of steam technology
in the late eighteenth century. Hence, the results ought to be regarded with care,
taking into account not only the possible influence of factors not included in our set
Table 3 Adoption of Newcomen engines 1775–1800: negative binomial regressions
(1) (2) (3) (4)
Type NB 1 NB 2 NB 1 NB 2
Constant 2.762***
(0.464)
2.887***
(0.530)
1.272***
(0.258)
1.094***
(0.339)
Coal price -0.119***
(0.0372)
-0.136***
(0.0372)
Coal dummy -1.968***
(0.376)
-2.163***
(0.414)
Water-wheels 0.00193
(0.00177)
0.00301
(0.00223)
0.00375**
(0.00186)
0.00454*
(0.00258)
Blast furnace 0.0130
(0.0179)
0.0103
(0.0284)
0.00563
(0.0165)
-0.0155
(0.0379)
Cotton mills 0.000277
(0.00611)
0.00224
(0.00923)
0.00198
(0.00588)
0.0105
(0.0136)
Wool mills -0.0160*
(0.00820)
-0.0251**
(0.0102)
-0.0156*
(0.00849)
-0.0121
(0.0121)
Coal output 0.000636***
(0.000215)
0.000672*
(0.000369)
0.000928***
(0.000158)
0.00104**
(0.000447)
Steam patents 0.164**
(0.0691)
0.224*
(0.115)
0.183**
(0.0836)
0.293***
(0.110)
Population 0.00160
(0.00259)
0.000826
(0.00360)
0.000567
(0.00226)
0.000210
(0.00280)
Industry dummy -0.587
(0.410)
-0.949
(0.670)
Log-likelihood -109.9 -118.0 -157.1 -169.2
Pseudo R2 0.214 0.155 0.227 0.168
Number of counties 41 41 84 84
Dependent variable is the number of Newcomen engines installed in the period 1775–1800. Standard
error in brackets. *, **, *** indicate significance levels of 10, 5, and 1 percent
The early diffusion of the steam engine in Britain 311
123
of explanatory variables, but also that the interpretation of the coefficients of the
variables included in the econometric model is by no means straightforward.
Tables 3 and 4 report our estimates for the equations having as dependent
variable the number of engines. We have estimated the coefficients considering two
different forms of the negative binomial density function. In the first case we have
assumed a density function with mean equal to l and variance equal to l(1 ? d).
This case is termed ‘‘NB 1’’ by Cameron and Trivedi (1998, p. 62). In the second
case we have assumed that the negative binomial density function has mean equal to
l and variance equal to l(1 ? al). Cameron and Trivedi (1998, p. 62) refer to this
model as ‘‘NB 2’’. It is possible to test for the actual existence of ‘‘overdispersion’’
(i.e., that the variance is larger than the mean) by verifying that a or d are different
from zero. In our case this was done by means of a likelihood ratio test (Cameron
Table 4 Adoption of Boulton & Watt engines 1775–1800: negative binomial regressions
(1) (2) (3) (4)
Type NB 1 NB 2 NB 1 NB 2
Constant 1.386***
(0.427)
1.838***
(0.486)
0.891***
(0.311)
0.669
(0.408)
Coal price -0.00943
(0.0200)
-0.0449
(0.0274)
Coal dummy -1.332***
(0.406)
-1.943***
(0.544)
Water-wheels -0.000564
(0.00191)
-0.00339
(0.00279)
-0.00157
(0.00233)
-0.00413
(0.00351)
Blast furnaces 0.0495***
(0.0167)
0.0525*
(0.0317)
0.0482**
(0.0198)
0.00864
(0.0435)
Cotton mills 0.00784
(0.00558)
0.00277
(0.00857)
-0.00417
(0.00536)
-0.00871
(0.0102)
Wool mills -0.0110
(0.00927)
-0.00935
(0.0104)
-0.0146
(0.0105)
-0.0157
(0.0135)
Coal output 0.000722***
(0.000223)
0.000372
(0.000342)
0.000678***
(0.000212)
0.000377
(0.000461)
Steam patents 0.105
(0.0764)
0.108
(0.102)
-0.0208
(0.0773)
0.395**
(0.157)
Population 0.00148
(0.00231)
0.00525
(0.00362)
0.00579***
(0.00216)
0.00988**
(0.00385)
Industry dummy 0.533
(0.380)
0.100
(0.634)
Log-likelihood -119.8 -123.4 -154.5 -163.4
Pseudo R2 0.150 0.124 0.205 0.159
Number of counties 41 41 84 84
Dependent variable is the number of Watt engines installed in the period 1775–1800. Standard error in
brackets. *, **, *** indicate significance levels of 10, 5, and 1 percent
312 A. Nuvolari et al.
123
and Trivedi 1998, pp. 77–78) that has confirmed the existence of overdispersion
supporting our choice of negative binomial estimations.
In this respect, one can note that the existence of overdispersion points to the fact
that the data exhibit a higher degree of cross sectional heterogeneity (i.e. clustering
in counties with ‘‘high’’ or ‘‘low’’ number of engines), than the case of a spatially
homogeneous Poisson process. In other words, the existence of overdispersion
reveals a pattern of spatial clustering among counties in terms of their extent of
steam usage that goes beyond what can be accounted for by our set of explanatory
variables. One could actually suggest that this cross-sectional heterogeneity can be
seen as providing an indication of the existence of county-specific absorptive
capabilities affecting the spread of steam technology. In general the NB 1 model
should probably be the preferred specification in terms of goodness of fit (pseudo
R2), but it is worth noting the coefficients estimated using the NB 1 and NB 2 are
consistent with each other.
The price of coal (whose inclusion restricts the sample to 41 counties) is
negative and significant in the case of Newcomen engines, where is not
significant in case of Watt engines. The marginal effect of the estimated
coefficient in the NB 1 specification implies that an increase of the price of coal
of 1 shilling would determine a reduction of 0.7 Newcomen engines installed in
the county. The coefficient for the coal dummy is negative and significant both
for Newcomen and Watt engines. As one could have expected, the negative size
of the coefficient for Newcomen engine is larger than the one for Watt engines.
In this case, the marginal effects of the estimated coefficients in the NB 1
specification imply that being a high coal price county determines a reduction of
6.2 Newcomen and of 3.6 Watt engines in comparison with a low coal price
county with the same characteristics. Our findings, thus, confirm the role of coal
prices as the critical variable affecting the choice between Newcomen and Watt
engines in our cross-section of counties. Note that the variable coal output has
also a positive and significant coefficient of roughly similar size both in Tables 3
and 4.
Curiously enough, in Table 3 the coefficient for number of wool mills variable is
significant with a negative sign. This can be accounted for by the peculiarities of the
transition to steam power mechanization in the wool textile industry (which was
concentrated in Yorkshire (West Riding) and in the West of England). Overall the
shift to steam in wool textiles was much slower than in cotton. Furthermore, in this
industry, the diffusion of steam technology proceeded at two very different paces in
the two areas. In West Riding, atmospheric returning engines were rapidly and
rather successfully adopted for power carding and spinning machines (jennies).
Table 2 indicates that about Newcomen 100 engines were installed in West Riding
by 1800. Instead in the other wool regions of the West of England (Gloucester,
Wiltshire) and of Scotland, steam power technology was introduced very slowly
(Jenkins and Ponting 1982, pp. 50–56). The combined effect of these two
contrasting patterns of adoption can help explain why the coefficient for wool mills
appears significant with a negative sign in some specifications.
In Table 3 the variable ‘‘steam patents’’ has a positive and significant coefficient,
showing the positive influence of the level of engineering skills for the adoption of
The early diffusion of the steam engine in Britain 313
123
engines.24 The marginal effect of this coefficient in the NB 1 specification of
column 3 implies that having one more patent in steam engineering would
determine an increase of 0.4 Newcomen engines installed in the county. There does
not seem, instead, to exist a systematic relation between the number of Watt engines
and the number of steam patents (the variable is significant only in column 4 of
Table 4). This is actually consistent with the fact that Watt engines throughout the
eighteenth century (with the exception of ‘‘pirate’’ engines) were installed by only
one company owning a proprietary technology.
Finally the coefficient of the variable water-wheels is positive and significant in
the models estimated in columns 3 and 4 of Table 3, whereas the variable is not
significant in Table 4. This result may probably be accounted for by the fact that
Newcomen engines delivering rotary motion where often used to pump water for a
wheel, whereas Watt engines were more frequently employed providing directly
rotary motion (Hills 1989).
In Table 4, the positive and significant coefficient for the variable blast furnaces
in the equations for Watt engines is consistent with those historical accounts that
have emphasized the rapid adoption of the engine in ironworks type of application
(Hyde 1977). The marginal effect of the coefficient estimated using the NB 1 model
in column 3 implies that having one more blast furnace would determine an increase
of 0.35 Watt engines installed in the county.
6 Concluding remarks
In this paper we have provided a reconstruction of the patterns of diffusion and
adoption of steam engine technology during the eighteenth century. Furthermore we
have also attempted to assess the influence of various explanatory factors on the
diffusion process. Our findings indicate that the level of coal prices was indeed one
of the major determinants of the distinctive patterns of adoption of Newcomen and
Watt engines, giving further support to the previous studies of von Tunzelmann
(1978) and Kanefsky (1979). In a broader perspective, this link between coal prices
and the intensity of steam power usage is also consistent with Allen (2009) who
argues that the successful development of steam power technology in a global
perspective can be seen as an outcome of Britain’s price structure of relative high
wages and cheap coal prices combined with a substantial endowment of engineering
skills. Our results, shows that, although this view is broadly accurate, spatial
variations in coal prices within Britain are also a part of the story.
However, it is also clear that, together with the level of coal prices, a number of
other factors were also at work. In this respect it must be also acknowledged that
Newcomen and Watt are rather ‘‘broad’’ categories. The specific design of the
engine did not only determine its fuel efficiency, but also the quality of the power
delivered (smoothness and regularity of motion, susceptibility to breakages,
24 We have also estimated specifications including as explanatory variable the total number of patents
granted over the period 1700–1800 (this may be though to capture a general level of inventive skills,
rather than those related with steam engineering), but the variable was not significant.
314 A. Nuvolari et al.
123
easiness of maintenance etc.). Not surprisingly, particular engine designs turned out
to better suited for specific applications than others (in some cases, despite their
level of fuel efficiency). This issue is discussed more in detail in Frenken and
Nuvolari (2004).
Our econometric analysis also indicates that, in the course of the eighteenth
century, the regional patterns of usage of steam technology displayed considerable
spatial diversity, reflecting the direct influence of locational determinants such as
the price of coal and the production structure of the various counties, but, possibly,
also of more complex and idiosyncratic factors impinging on the capabilities of the
individual counties of absorbing the new technology of steam power (as revealed by
the existence of ‘‘overdispersion’’ in the negative binomial estimations). In a more
general perspective, this finding confirms the need of taking regional differences
properly into account when examining the process of technical change during the
British industrial revolution (Hudson 1989).
Acknowledgments We would like to thank John W. Kanefsky for providing us with the updated
version of his dataset of eighteenth century British steam engines. We are also grateful to Joel Mokyr,
Christine MacLeod, Tine Bruland, Jeremy Atack, Onder Nomaler, Roberto Fontana, Liam Brunt and two
anonymous referees for helpful comments on previous versions of this paper. The research of Alessandro
Nuvolari has been partially funded by Netherlands Organization for Scientific Research (Veni Grant,
‘‘Inventive activities, patents and the industrial revolution’’).
Open Access This article is distributed under the terms of the Creative Commons Attribution Non-
commercial License which permits any noncommercial use, distribution, and reproduction in any med-
ium, provided the original author(s) and source are credited.
Appendix 1: The Moran I statistic
Moran I statistic is essentially a correlation coefficient which assesses the degree of
spatial autocorrelation of a spatial variable. Assume that the variable x is defined
over a number locations n. We can construct a matrix W (spatial contiguity matrix)
which indicates whether two counties have borders in common or not. The matrix is
symmetric and each element wij is equal to 1 when the locations i and j a border in
common and to 0 otherwise. The elements on the main diagonal of the contiguity
matrix are equal to 0. In this case Moran I statistic is equal to
I ¼ n
Pn
i¼1
Pn
j¼1 ziwijzj
2  Pni¼1
Pn
j¼1 wij
 
Pni¼1 z2i
where is zi ¼ xi  x (the deviation of xi from the mean). Higher values of I indicate
a stronger degree of (positive) spatial autocorrelation. Cliff and Ord (1981,
pp. 42–46) illustrate how to compute significance intervals for Moran’s I under two
different hypotheses: the first one is that the observations x are normally distributed
(normality assumption) whereas the second one (randomised) assumes that the
realizations of x were extracted from one of the possible n! permutations of the
n values of the variable x over the n locations.
The early diffusion of the steam engine in Britain 315
123
Appendix 2: Estimates of diffusion rates
Table 5 Estimates of diffusion curves
County Newcomen Boulton & Watt
K a b T R2 K a b T R2
Cheshire 23
(3)
0.220
(0.025)
1795
(1)
0.99
Cornwall 75
(4)
0.186
(0.101)
1767
(1)
2.98
(1.83)
0.99 56
(4)
0.173
(0.103)
1781
(1)
-0.40
(0.64)
0.99
Cumberland 564
(374)
0.039
(0.012)
1878
(325)
0.97
Derby 98
(9)
0.054
(0.003)
1791
(3)
0.99
Durham 112
(7)
0.059
(0.005)
1771
(3)
0.97 18
(1)
0.910
(0.145)
1796
(1)
0.99
Gloucester 55
(2)
0.083
(0.005)
1770
(1)
0.99
Lancashire 644
(242)
0.347
(0.256)
1827
(14)
5.60
(3.90)
0.90 697
(1)
1.448
(0.120)
1810
(1)
7.04
(0.88)
0.98
Leicester 12
(1)
0.056
(0.005)
1771
(3)
1.00
London 293
(1)
0.253
(0.016)
1855
(2)
8.83
(0.39)
0.98 95
(12)
0.182
(0.022)
1794
(2)
0.98
Northumberland 169
(12)
0.063
(0.005)
1773
(3)
0.97 57
(64)
0.249
(0.088)
1802
(8)
0.98
Nottingham 110
(13)
0.215
(0.528)
1848
(11)
6.54
(17.71)
0.96 18
(1)
0.636
(0.108)
1789
(1)
0.97
Shropshire 205
(104)
0.038
(0.005)
1818
(21)
0.98 45
(2)
0.253
(0.022)
1786
(1)
0.98
Stafford 61
(9)
0.764
(1.288)
1795
(5)
25.06
(42.03)
0.99 43
(2)
0.186
(0.012)
1788
(1)
0.99
Warwick 46
(9)
0.034
(0.008)
1760 0.91 39
(76)
0.117
(0.050)
1808
(26)
0.96
Worcester 26
(4)
0.396
(0.064)
1833
(2)
18.57
(0.40)
0.91
West riding 261
(1)
0.819
(0.041)
1816
(1)
16.21
(0.75)
0.99 47
(25)
0.224
(0.053)
1799
(4)
0.97
Flint 19
(2)
0.043
(0.224)
1732
(12)
-0.31
(3.49)
0.98
Glamorgan 13
(1)
0.116
(0.018)
1763
(1)
0.97
316 A. Nuvolari et al.
123
Appendix 3: Sources and construction of the data
Number of steam engines (‘‘atmospheric’’ and Boulton & Watt) installed during the
period 1775–1800: Data taken from the updated version of the Kanefsky and
Robey (1980) list.
Price of Coal, c. 1800: Data taken from von Tunzelmann (1978, p. 148). The 41
counties for which coal prices were available are:
Cornwall, Devon, Wiltshire, Hampshire, Berkshire, Surrey, Middlesex (London),
Kent, Cambridge, Northampton, Oxford, Leicester, Warwick, Worcester,
Gloucester, Monmouth, Glamorgan, Shropshire, Stafford, Anglesey, Caernarvon,
Denbigh, Cheshire, Derby, Nottingham, Lancashire, East Riding, West Riding,
North Riding, Durham, Northumberland, Cumberland, Ayr, Renfrew, Lanark,
Stirling, Argyll, Clackmannan, Midlothian, Fife, Angus.
Coal dummy, c. 1800: The variable distinguishes between ‘‘cheap’’ and ‘‘dear’’
coal counties. Counties with coal prices higher than 16 s. per ton are considered as
having a ‘‘high’’ price of coal. The counties have been assigned on the basis of the
price list in von Tunzelmann (1978, p. 148) and of the maps and discussion of Flinn
(1984), von Tunzelmann (1986) and Turnbull (1987).
Low coal price counties: Cheshire, Cumberland, Derby, Durham, Lancashire,
Leicester, Monmouth, Northumberland, Nottingham, Shropshire, Stafford, War-
wick, Worcester, West Riding, East Riding, Carmarthen, Denbigh, Flint, Glamor-
gan, Pembroke, Angus, Ayr, Berwick. Clackmannan, Dunbarton, East Lothian, Fife,
Kinross, Lanark, Midlothian, Renfrew, Stirling, West Lothian.
High coal price counties: Bedford, Berkshire, Buckingham, Cambridge, Cornwall,
Devon, Dorset, Essex, Gloucester, Hampshire, Hereford, Hertford, Huntingdon,
Kent, Lincoln, Middlesex (London), Norfolk, Northampton, Oxford, Rutland,
Somerset, Suffolk, Surrey, Sussex, Westmorland, Wiltshire, North Riding,
Table 5 continued
County Newcomen Boulton & Watt
K a b T R2 K a b T R2
Ayr 32
(5)
0.939
(1.77)
1795
(3)
18.25
(35.91)
0.98
Fife 113
(7)
0.507
(0.093)
1824
(8)
8.85
(1.12)
0.87
Lanark 37
(8)
0.122
(0.027)
1792
(4)
0.95
Stirling 60
(1)
0.537
(0.037)
1818
(1)
10.83
(0.17)
0.97
Standard errors in brackets. When T is not given, the standard symmetric logistic equation was estimated,
otherwise the generalized form (Richards growth equation) was used. The symmetric logistic has ana-
lytical standard errors, whereas the generalized form has bootstrapped standard errors
The early diffusion of the steam engine in Britain 317
123
Anglesey, Brecknock, Caernarvon, Cardigan, Merioneth, Montgomery, Radnor,
Aberdeen, Argyll, Banff, Caithness, Dumfries, Inverness, Kincardine, Kircudbright,
Moray, Nairn, Peebles, Perth, Ross and Cromarty, Roxburgh, Selkirk, Sutherland,
Wigtown.
Steam engineering patents, 1700–1800: Steam patents are taken from Abridg-
ments of Specifications relative to the Steam Engine, London, 1871. In order to
retrieve the stated residence of the patentees, these patents have been matched with
those contained in B. Woodcroft, Titles of Patents of Invention Chronologically
Arranged, London, 1854.
Coal output in 1800: Data (in 000s of tons) are taken from Flinn (1984),
pp. 26–27.
Population in 1801: Data for English counties are taken from Wrigley (2006).
Welsh and Scottish counties are taken from Comparative Statement of the Popu-
lation of the Several Counties of Great Britain in the years 1801 and 1811 (London,
House of Commons, 1812).
Water-wheels, c.1800: Data taken from Kanefsky (1979), pp. 215–216. The data
have been constructed on the basis of contemporary maps (i.e. they are presumably
likely to underestimate the actual figures). For more details, see Kanefsky (1979).
Blast furnaces, c. 1800: Data taken from Scrivenor (1854). The original source is a
government survey after the proposal of a tax on coal. The data refer to the year
1796. For a discussion of this source, see Evans (1993).
Cotton Mills, c. 1800: Data taken from Chapman (1970, pp. 257–266). Chapman’s
figures are based on insurance records and they mostly refer to the year 1795. For
Lancashire we have estimated a figure of 204 mills, which is based on the
assumption that the county had 50% of large mills (types B and C) and 50% of type
A (i.e., small) mills. This is in line with the considerations contained in Chapman’s
paper.
Wool Mills, c. 1800: Data taken from Chapman (1970, pp. 257–266). Chapman’s
figures are based on insurance records and they mostly refer to the year 1795. For
Lancashire we have estimated a figure of 204 mills, which is based on the
assumption that the county had 50% of large mills (types B and C) and 50% of type
A (i.e., small) mills. This is in line with the considerations contained in Chapman’s
paper.
Industry dummy, c. 1800: This dummy variable indicates the counties where in
the second half of the eighteenth century manufacturing employment was growing
fastest (Wrigley 2006, p. 19). We have considered also the ‘‘London group’’
(London & Middlesex, Surrey and Kent) discussed by Wrigley as a separate group
as belonging to this industrial group (Table 6).
318 A. Nuvolari et al.
123
References
Allen RC (2009) The British industrial revolution in global perspective. Cambridge University Press,
Cambridge
Atack J, Bateman F, Weiss T (1980) The regional diffusion and adoption of the steam engine in American
manufacturing. J Econ Hist 40:281–308
Berg M, Hudson P (1992) Rehabilitating the industrial revolution. Econ Hist Rev 45:24–50
Birch CPD (1999) A new generalized logistic sigmoid growth equation compared with the Richards
growth equation. Ann Bot 83:713–723
Bresnahan T (2010) General purpose technologies. In: Hall BH, Rosenberg N (eds) Handbook of the
economics of innovation. Elsevier, Amsterdam, pp 761–791
Cameron AC, Trivedi PK (1998) Regression analysis of count data. Cambridge University Press,
Cambridge
Chapman SD (1970) Fixed capital formation in the British cotton industry, 1770–1815. Econ Hist Rev
23:235–266
Chapman SD (1971) The cost of power in the industrial revolution in Britain. The case of the textile
industry. Midl Hist 1:1–23
Cipolla CM (1962) The economic history of the world population. Harmondsworth, Penguin
Cliff AD, Ord JK (1981) Spatial processes: models and applications. Pion, London
Crafts N (2004a) Steam as a general purpose technology. A growth accounting perspective. Econ J
114:338–351
Crafts N (2004b) Productivity Growth In The Industrial Revolution. A new growth accounting
perspective. J Econ Hist 64:521–535
Crafts N, Harley K (1992) Output growth and the British industrial revolution: a restatement of the
Crafts–Harley view. Econ Hist Rev 45:703–730
Dickinson HW (1936) Matthew Boulton. Cambridge University Press, Cambridge
Dickinson HW, Jenkins R (1927) James Watt and the steam engine. Clarendon, Oxford
Dixon R (1980) Hybrid corn revisited. Econometrica 48:1451–1461
Dosi G (1984) Technical change and industrial transformation. The theory and an application to the
semiconductor industry. MacMillan, London
Evans C (1993) The statistical surveys of the British Iron industry in 1797–98 and in 1806. J Hist Metall
Soc 27:84–101
Flinn MW (1984) The history of the British coal industry, 1700–1830, vol II. Clarendon Press, Oxford
Frenken K, Nuvolari A (2004) The early development of the steam engine: an evolutionary interpretation
using complexity theory. Ind Corp Change 13:419–450
Geroski PA (2000) Models of technology diffusion. Res Policy 29:603–625
Table 6 Descriptive statistics
Variable Mean Min Max SD
Newcomen engines, 1775–1800 7.297619 0 72 15.22109
Boulton & Watt engines, 1775–1800 6.392857 0 90 16.42142
Price of coal in s., c. 1800 16.71341 6.333333 46.66667 10.43959
Coal dummy 0.607143 0 1 0.491319
Water mills, c. 1800 118.631 10 700 108.2037
Blast furnaces, c. 1800 1.380952 0 23 4.315578
Cotton mills, c. 1800 5.214286 0 204 23.97492
Wool mills, c. 1800 5.380952 0 102 15.81817
Steam patents, 1700–1800 0.869048 0 21 2.687677
Coal output (in 000 of tons), c. 1800 179.1071 0 2,225 439.018
Industry dummy 0.119048 0 1 0.32579
Population in 1801 (in 000s) 128.5435 5.07 855.615 142.9887
The early diffusion of the steam engine in Britain 319
123
Greene WH (2000) Econometric analysis, 4th edn. Prentice-Hall, Upper Saddle River
Griliches Z (1957) Hybrid corn: an exploration in the economics of technological change. Econometrica
25:501–522
Grubler A (1990) The rise and fall of infrastructures. Dynamics of evolution and technical change in
transport. Physica-Verlag, Heidelberg
Hills RL (1970) Power in the industrial revolution. Manchester University Press, Manchester
Hills RL (1989) Power from steam. A history of the stationary steam engine. Cambridge University Press,
Cambridge
Hills RL (2002) James Watt: his time in Scotland, 1736–1774. Landmark, Ashbourne
Hudson P (1989) The regional perspective. In: Hudson P (ed) Regions and industries: a perspective on the
industrial revolution in Britain. Cambridge University Press, Cambridge
Hunt EH (1986) Industrialization and regional inequality: wages in Britain, 1760–1913. J Econ Hist
46:935–966
Hyde CK (1977) Technological Change and the British Iron Industry, 1700–1870. Princeton University
Press, Princeton
Jenkins DT, Ponting KG (1982) The British wool textile industry, 1770–1850. Heinemann, London
Kanefsky JW (1979) The diffusion of power technology in British industry, 1760–1870. PhD Thesis,
University of Exeter
Kanefsky JW, Robey J (1980) Steam engines in 18th century Britain: a quantitative assessment. Technol
Cult 21:161–186
Landes DS (1969) The unbound prometheus. Technological change and industrial development in
Western Europe from 1750 to the present. Cambridge University Press, Cambridge
Langton J (1984) The industrial revolution and the regional geography of England. Trans Inst Brit Geogr
9:145–167
Lipsey R, Carlaw K, Bekar C (2005) Economic transformations. General purpose technologies and long
term economic growth. Oxford University Press, Oxford
Lissoni F, Metcalfe JS (1994) Diffusion of innovation ancient and modern: a review of the main themes.
In: Rothwell R, Dogdson M (eds) Handbook of industrial innovation, Edward Elagar, Aldershot
Musson AE, Robinson EH (1969) Science and technology in the industrial revolution. Manchester
University Press, Manchester
Nuvolari A, Verspagen B (2009) Technical choice, innovation and British steam engineering, 1800–1850.
Econ Hist Rev 62:685–710
Nuvolari A, Verspagen B, von Tunzelmann GN (2006) The diffusion of the steam engine in eighteenth
century Britain. In: Pyka A, Hanusch H (eds) Applied evolutionary economics and the knowledge
based economy. Edward Elgar, Aldershot
Pollard S (1981) Peaceful conquest. The industrialization of Europe 1760–1970. Oxford University Press,
Oxford
Richards FJ (1959) A flexible growth function for empirical use. J Exp Bot 10:290–300
Roll E (1930) An early experiment in industrial organisation. Being a history of the firm of Boulton &
Watt, 1775–1805. Longman, London
Rolt LTC, Allen JS (1997) The steam engine of Thomas Newcomen, 1st edn. Landmark, Ashbourne
Rostow WW (1960) The stages of economic growth. A non-communist manifesto. Cambridge University
Press, Cambridge
Rowlands MB (1969) Stonier Parrot and the Newcomen Engine. Trans Newcomen Soc 41:49–67
Scrivenor H (1854) History of the iron trade. Longmans, London
Smith A (1978) Steam and the city: the Committee of Proprietors of the Invention for Raising Water by
Fire, 1715–1735. Trans Newcomen Soc 49:5–20
Stoneman P (2002) The economics of technological diffusion. Blackwell, Oxford
Tann J (1988) Fixed capital formation in steam power, 1775–1825. A case study of the Boulton and Watt
engine. In: Feinstein CH, Pollard S (eds) Studies in capital formation in the United Kingdom,
1750–1920. Clarendon Press, Oxford
Trinder B (1973) The industrial revolution in Shropshire, Phillipmore, Chichister
Turnbull G (1987) Canals, coal and regional growth during the industrial revolution. Econ Hist Rev
40:537–560
von Tunzelmann GN (1978) Steam power and British industrialization to 1860. Clarendon, Oxford
von Tunzelmann GN (1986) Coal and steam power. In: Langton J, Morris RJ (eds) Atlas of industrializing
Britain. Methuen, London
Westworth OE (1933) The Albion Steam Flour Mill. Econ Hist 2:380–395
320 A. Nuvolari et al.
123
Wrigley EA (1988) Continuity, chance and change. The character of the industrial revolution in England.
Cambridge University Press, Cambridge
Wrigley EA (2004) Poverty, progress and population. Cambridge University Press, Cambridge
Wrigley EA (2006) English county populations in the later eighteenth century. Econ Hist Rev 65:1–41
The early diffusion of the steam engine in Britain 321
123