¹ Burn, Duncan L., The Economic History of Steelmaking, 1867–1939 (Cambridge: Cambridge University Press, 1961), pp. 183–84Google Scholar, 188–90. See also Temin, P., Iron and Steel in Nineteenth Century America (Cambridge: M.I.T. Press, 1964), pp. 157–63Google Scholar, for a more careful discussion of fast driving in America.

² McCloskey, Donald N., Economic Maturity and Entrepreneurial Decline (Cambridge: Harvard University Press, 1974), pp. 77–84, 114–20.Google Scholar

³ See Allen, Robert C., “International Competition and the Growth of the British Iron and Steel Industry, 1830–1913,” (doctoral dissertation, Harvard University, 1975), pp. 416Google Scholar, for average shares for Belgium, France, Britain, and the United States. The shares quoted in the text are British shares, and they are approximate averages of all shares. The British shares are taken from McCloskey, p. 83, n. 13.

⁴ Blast furnace fuel consumption data for most countries in the post-World War II period is summarized in the British Iron and Steel Federation, Statistical Handbook, 1964, volumes I and II. Earlier data is readily available in the statistical year book or mineral statistics of the country concerned.

⁵ Bell, I. Lowthian, Principles of the Manufacture of Iron and Steel (London, George Routledge & Sons, 1884), pp. 95–96Google Scholar. This “theoretical minimum” is meant to apply to commercially operating blast furnaces and to serve as a standard for gauging their absolute efficiency. It is thus based on the standard (and, as far as one can tell, optimal) ore and flux consumption. Bell's “theoretical minimum” also includes allowances for normal heat losses due to radiation and the escape of heated gasses.

⁶ German fuel consumption figures are not plotted in Figure 1 since the official mineral statistics did not record this information before 1908. However, the records of two firms indicate a pattern of productivity growth like that of France and Britain. For the records of the Gutehoffnungshütte, see Arnold Woltzmann, “Geschichte der Gutehoffnungshütte,” in Die Gutehoffnungshütte, Oberhausen, Rheinland, 1810–1910, no publisher, no date. For the records of the Georgs-Marienhütte, see Germany, Eisen-Enquette-Kommission, Protokolle über die Vernehmungen der Sachverständigen durch die Eisen-Enquette-Kommission, p. 272.

⁷ Another mid-nineteenth century anomaly is the low fuel consumption of the Belgian iron industry. This paper does not attempt to account for that peculiarity.

⁸ Figure 2 overstates the difference between American and British labor productivity and perhaps also the difference between labor productivity in America and on the Continent. The difficulty is that the average number of workers employed is a defective measure of the labor input since the workweek varied. For most of the nineteenth century the standard workweek for most blast furnace workers was 84 hours. This workweek remained standard in the American industry until the 1920s, but it began to decrease in Britain by 1890. Correcting the British labor measure for this decline raises British labor productivity to the American level for the period 1894–1913. See Allen, pp. 188–95. No investigation of the workweek of Continental ironworkers has been undertaken, although it is unlikely that variations in the workweek could account for all of the difference in output per worker. The implications of this measurement problem for efficiency comparisons will be noted as they arise.

⁹ See, for example, the following breakdowns of blast furnace construction costs: “Description of Two Blast Furnaces, erected in 1870, at the Newport, Middlesbrough,” Journal of the Iron and Steel Institute, 1871, pp. 382–88; Sir B. Samuelson, “Notes on the Construction and Cost of Blast Furnaces in the Cleveland District in 1887,” ibid., 1887, vol. I, pp. 91–119; and Jno. L. Stevenson, “The Design and Equipment of Blast Furnaces,” The Engineer, 1902.

¹⁰ See Allen, p. 64.

¹¹ See, for instance, William Hawdon, “Notes on American Blast Furnace Practice, and a Comparison with the Work Done in the Cleveland District,” Proceedings of the Cleveland Institution of Engineers, 1891, pp. 171–90.

¹² Define the relative change in total factor productivity in instances 1 and 2 to be

where A₁ is the index, Q₁ is actual output in instance i, and f(X¹) equals what output would be if the production function were unchanged in the two instances. is the vector of inputs in instance i. Diewert, W. E., “Exact and Superlative Index Numbers,” Journal of Econometrics, 4 (1976), pp. 115–45, has shown thatCrossRefGoogle Scholar

where is the share in costs of the jth input in the ith instance, if f is a translog production function and there is cost minimization. The assumption of a translog production function is useful since such a function provides a second order approximation to any constant returns to scale production function. Performing the indicated division,

that is, A2/A1 equals a weighted geometric average of the relative average products of the inputs where the weights are the average shares in two instances. Since there was little variation in the shares, the exponents shown in equation 1 were used for all calculations. Little error is introduced with this approximation.

Equation 1 is superior to McCloskey's total factor productivity index since the value of that index depends on the change in industry output as well as the change in average products. McCloskey's index, given in Economic Maturity, p. 143, can be written as

where asterisks indicate proportional changes and the notation has been made consistent with that used here. McCloskey's index can be shown to equal

when the proportions are calculated with respect to the first instance. Changes in this index clearly depend on changes in the industry's output (Q₂/Q₁) as well as on changes in the average products. If the ore term is deleted, these conclusions still obtain.

¹³ When measuring the growth in productivity in one country, there is a plausible alternative approach to the capital measurement problem. Since capital per furnace increased during the nineteenth century, a time series of the number of furnaces in blast is a lower bound measure of the capital stock. If the number of furnaces in blast is used to measure the capital stock in equation 1, the computed growth in total factor productivity will be on upper bound to the actual growth. The growth in efficiency in European countries was computed in this manner. While the growth rates were always a bit higher, the underlying patterns were the same as those in Table 1. Unfortunately, this approach to the capital measurement problem is no help in international comparisons of the level of efficiency.

¹⁴ In constructing Table 2, the British and American labor inputs were measured in “manyears” and “average numbers of workers employed,” respectively. These units are equivalent, as indicated in footnote 8 and Allen, p. 188–95. The labor inputs on the Continent were also measured as “average number of workers employed,” but these units represent less labor than the others if the workweek on the Continent was less than in America. Assuming the Continental workweek to be the same as Britain's, A_E/A_A equals 93 for France, 1.00 for Belgium, and 96 for Germany in 1909.

¹⁵ In these calculations horsepower is used as the measure of capital. The trivial contribution of the growth in capital productivity to the growth in total factor productivity is a reflection of the constancy of the output-horsepower ratio.

¹⁶ Burn, pp. 183–84, 188–90.

¹⁷ American Iron Association, Bulletin, p. 59.

¹⁸ See Peter Temin, Iron and Steel, pp. 157–63, for a discussion of this process.

¹⁹ Calculated from the returns for Pennsylvania in the manufacturing schedules of the 1870 United States Census.

²⁰ See, for instance, Frazier, B. W., “Economy of Fuel in Our Anthracite Blast-Furriaces,” Transactions of the American Institute of Mining Engineers, III, 1874–5, 158Google Scholar. A direct estimate of limestone consumption per ton of pig iron can be made for Britain's principal pig iron producing districts. The South Wales, South Staffordshire, Cleveland, and Scotland districts produced 74 percent of Britain's pig iron in 1870. (Mitchell, R. B. and Deane, P., Abstract of British Historical Statistics, [Cambridge: Cambridge University Press, 1971], p. 132Google Scholar). Gruner, M. and Lan, M., État présent de la métallurgie du fer en Angleterre (Paris, 1862), pp. 160–61Google Scholar, estimate limestone consumption per ton of pig iron. Using 1870 production figures as weights, average limestone consumption per ton of pig iron was 59 tons in those four districts.

²¹ Gordon, Fred W., “American Blast Furnace Practice, With Special Reference to the Works of the North Chicago Rolling-Mill Co. at South Chicago, Illinois,” Journal of the Iron and Steel Institute, 1886, II, 779–90Google Scholar, and Potter, E. C., “The South Chicago Works of the North Chicago Rolling-Mill Company,” Journal of the Iron and Steel Institute, 1887, I, 163–79.Google Scholar

²² No attempt was made to explain either the average product capital, since that scarcely changed, or the average product of ore, since that depended on the composition of the ore, not the blast furnace technology.

²³ The sources of the data are listed and described in Allen, pp. 410–18. Since charcoal technology was so different from mineral fuel technology, the charcoal sector had to be eliminated from the data before the regressions were run. This elimination was accomplished in two steps. First, all states in which charcoal iron accounted for more than 10 percent of the total production were eliminated. This was a complete solution to the problem for the years after 1880, since for those years the remaining states produced virtually no charcoal iron. Second, for the states in 1880 that were not eliminated, estimates were made, on the basis of 1870 census schedules, of the use of flux, horsepower, and furnace stacks in the charcoal sector, and these estimates were subtracted from the statewide figures to get estimates of the resources used in the, mineral fuel sector. These estimates were the data used in the regressions. The 29 states in the sample were: 1879-Ill., Ind., N.J., Pa., W. Va.; 1889-Ill., N.J., Ohio, Pa., W. Va.; 1899-Ill., Md., N.J., N.Y., Ohio, Pa., W. Va., other; 1904-Ill., N.J., N.Y., Ohio, Pa., other; 1909-Ill., N.Y., Ohio, Pa., other.

²⁴ The 1879 figures are calculated from the estimates for the mineral fuel sector for the states used in the regression.

²⁵ United States Bureau of Labor Statistics, Productivity of Labor in Merchant Blast Furnaces, Bulletin No. 474, 1928, p. 22, indicates that 46 percent to 50 percent of the sampled merchant blast furnaces operating in 1911–14 had slap charging equipment. The Bureau regarded its pre-war sample as biased toward high productivity furnaces, but it emphasized the high use of pig casting machines in its discussion of this point. Ibid., pp. 6–7. Half of the active furnaces in 1912–14 were merchant furnaces; the remainder were integrated with steel works. Ibid., p. 138. The steelworks blast furnaces have always been reputed to be the most innovative. Temin, pp. 160, 162. If half of the merchant furnaces used skip charging machines, while all of the steelworks furnaces did, then 75 percent of America's blast furnaces had such machines. If the steelworks furnaces were not more efficient than die merchant furnaces, then 50 percent of the nation's furnaces used slap charging machines.

²⁶ U.S. Census Bureau, Census of Manufactures, 1914, vol. II, p. 211Google Scholar. The remaining iron—2.8 percent in 1910—was either chill cast or cast as final products at the blast furnace.

²⁷ United States Bureau of Labor Statistics, Productivity of Labor in Merchant Blast Furnaces, Bulletin No. 474, 1928.

²⁸ The data are taken from Productivity … in Merchant Blast Furnaces, pp. 109–10, 113–15. Skip charging and pig casting machines were quite small in relation to the blowing apparatus, so they also had little effect on capital or horsepower per furnace and per ton of pig iron. On casting machines, see, for instance, Wainford, R. H., “A new Casting-Machine for Blast-Furnaces,” Journal of the Iron and Steel Institute, 1899, II, 53–57Google Scholar. Skip charging machines replaced older-style hoists and hoist engines which would have been required to perform the same mechanical work and which consequently would have been of similar horsepower. The construction cost estimates for alternative blast furnace designs given in Jno. L. Stevenson, “The Design and Equipment of Blast Furnaces,” The Engineer, 1902, suggest, moreover, that there was no increase and perhaps even a slight reduction in capital requirements by this change in technique.

²⁹ Ibid., p. 47.

³⁰ Output per furnace was computed from the sources listed in Allen, pp. 417–18.

³¹ See Temin, Peter, “The Relative Decline of the British Steel Industry, 1880–1913,” in Rosovsky, Henry, ed., Industrialization in Two Systems (New York, 1966), pp. 140–55Google Scholar, and McCloskey, pp. 105–13.

³² In general, limestone consumption was only one determinant of blast furnace fuel consumption. Other determinants which have received considerable attention are the hot blast developed in the 1830s and the very tall blast furnace pioneered in England's Cleveland district in the 1860s. The place of the very tall blast furnace in the productivity history of iron smelting is considered in section IV.

³³ Frazier, B. W., “Economy of Fuel in Our Anthracite Blast-Furnaces,” Transactions of the American Institute of Mining Engineers, III, 1874–5, 157–72.Google Scholar

³⁴ Ibid., p. 159.

³⁵ Ibid., p. 159.

³⁶ Ibid., p. 159.

³⁷ Ibid., p. 160.

³⁸ Ibid., pp. 158, 161.

³⁹ U.S. Census Bureau, Ninth Census, 1870, Industry and Wealth, p. 768. Nine hundred thousand tons were added to the Pennsylvania total on the basis of the estimated underreporting, p. 749. U.S. Census Bureau, Mines and Quarries, 1902, pp. 402, 404–5.

⁴⁰ Campbell, Harry Huse, The Manufacture and Properties of Iron and Steel (New York: McGraw-Hill, 1907), p. 459.Google Scholar

⁴¹ Burdening calculations are discussed and illustrated in the following: McGannon, Harold E., The Making, Shaping and Treating of Steel (9th ed., United States Steel Corporation, 1971), pp. 467–68Google Scholar; Strassburger, J. H., Blast Furnace—Theory and Practice vol. 2.(New York, 1969), pp. 615–18Google Scholar. Camp, J. M. and Francis, C. B., The Making, Shaping, and Treating of Steel (2nd ed.; Pittsburgh, Carnegie Steel Co., 1920), pp. 161–63Google Scholar; Johnson, J. E. Jr., The Principles, Operation, and Products of the Blast Furnace (New York, 1918), pp. 266–71.Google Scholar

⁴² Camp and Francis, p. 162, and Johnson, p. 268, recommend higher slag ratios, but their ratios are defined as (CaO + MgO)/SiO₂. Al₂O₃ is excluded from the denominator. When this formula is applied to Lake ores, it gives the same result as the modern formula.

⁴³ In these calculations the pig iron was assumed to be 94 percent Fe and 2 percent Si; the limestone was assumed to be 49 percent CaO and MgO; the anthracite was assumed to be 4.3 percent SiO2 and 4.7 percent Al₂O₃; the coke was assumed to b e 4.4 percent SiO₂, 2.8 percent Al₂O₃, 25 percent CaO, and 15 percent MgO. These figures are taken from, respectively, Frazier, p. 162, Johnston, Principles, p. 268, Frazier, pp. 162–63, and Camp and Francis, p. 160.

⁴⁴ Frazier, p. 159, argued that limestone consumption was not excessive since the slag ratio was 1.03.

⁴⁵ These calculations assume one ton of coke was consumed per ton of pig iron. Even if two tons of coke were still used, 59 tons of limestone would be required when the slag ratio is 1.2 and 49 tons would be required if it equalled 1. The small change in the results show the insensitivity of the procedure to the value assumed for the coke rate.

⁴⁶ Bell, Principles, chs. V–X, establishes that increasing the height of a blast furnace smelting Cleveland iron stone to 80 feet significantly reduces the coke rate. Further increases in height have negligible effect on the coke rate. Bell also establishes that increases beyond 55–60 feet in the height of a blast furnace smelting other ores have little effect on fuel economy. Bell's conclusions are summarized in Principles, p. 145–46. Bell's conclusions are confirmed with econometric investigation in Allen, pp. 96–109. Between 1879 and 1909 there was scarcely a mineral fuel blast furnace in the United States less than 60 feet tall, so the fuel economies attendant upon increasing furnace height had been exhausted in the United States in that period. This result is comforting in that it implies the equations reported in Table 3 are not misspecified due to the exclusion of a height term.