Category Archives: history

The forgotten discovery of gravity models and the inefficiency of early railway networks

Andrew Odlyzko finds the earliest use of gravity models for travel demand and spatial interaction in his new working paper “The forgotten discovery of gravity models and the inefficiency of early railway networks“, moving the clock a few years earlier.

Abstract. The routes of early railways around the world were generally inefficient because the prevailing doctrine of the time called for concentrating on provision of fast service between major cities and neglect of local traffic. Modern planners rely on methods such as the “gravity models of spatial interaction,” which show the costs of such faulty assumptions. Such models were not used in the 19th century.
The first formulation of gravity models is usually attributed to Henry Carey in 1858. This paper shows that a Belgian civil engineer, Henri-Guillaume Desart, discovered them earlier, in 1846, based on the study of a unique and extensive data set on passenger travel in his country. His work was published during the great Railway Mania in Britain. Had the validity and value of this contri- bution been recognized properly, the investment losses of that gigantic bubble could have been lessened, and more efficient rail systems in Britain and many other countries would almost surely have been built. This incident shows society’s early encounter with the “Big Data” of the day and the slow diffusion of economically significant information. The methods used in the study point to ways to apply methods of modern network science to analyze information dissemination in the 19th century.

Lord Gordon-Gordon |

Cross-posted from Lord Gordon-Gordon.

Lord Gordon-Gordon (a.k.a. Lord Glencairn, Hon. Mr. Herbert Hamilton, George Herbert Gordon, George Gordon, George Hubert Smith, and John Herbert Charles Gordon) migrated from Britain to North America in 1870. He was not a Lord, as many Americans and Canadians later learned, merely impersonating a Scottish peer to borrow money to buy land. He landed in Minnesota in 1871, and deposited £20,000 in a local bank, establishing legitimacy. He promised to invest $5 million to help resettle 100 Scottish families on land managed for the Northern Pacific Railroad. Col. Loomis, the land commissioner for the Northern Pacific spent $45,000 touring with Lord Gordon-Gordon through rural Minnesota.

Lord Gordon-Gordon

“He who sells what isn’t his’n, must buy it back or go to pris’n.” – Daniel Drew (attributed)

Beginning with the New York & Harlem Railroad, Cornelius Vanderbilt started accumulating a network to connect New York with Chicago, which by 1870 comprised the New York Central & Hudson Railroad, then valued at $100,000,000, the most successful of the Northeast lines, which was able to pay dividends through the Panic of 1873. His methods were harsh. He cut off feeder traffic to force a downstream company into his control. He cornered the market in stocks to punish short-selling public officials.

Short-selling is selling stocks you don’t own with the hope of buying them back later at a lower price, and is in contrast with going long on a stock, or buying it with the expectation it will rise in price. Clearly if the price does not fall, a short-seller will lose money. If someone can acquire a majority of the outstanding stock, and an insufficient amount of stock is available for short-sellers to purchase, their losses can be astronomical. In one of his few failures, Vanderbilt got into a bidding war over the Erie Railroad.

The “Erie War” brought together a cast of some of America’s most important financiers and railroad men in a battle over a second-tier railroad.

Daniel Drew (1797-1879) was once Vanderbilt’s partner. He became a stock-broker in 1844, and joined the Board of the Erie RR in 1857. He shorted the stock of New York & Harlem RR, and lost a fortune in 1864. After the Erie War with Vanderbilt, in 1870 Fisk and Gould then played Drew, causing him to lose $1.5 million. The Panic of 1873 was no aid, and Drew filed for bankruptcy and died penniless.

James (Diamond Jim) Fisk (1835-1872) made his first fortune dealing in Army contracts in the US Civil War. While he lost this wealth in speculation, after the War he worked for Daniel Drew’s brokerage. The famous Black Friday of 1869 resulted from Fisk and Gould’s failed attempt to corner the Gold Market. After the Erie War, Fisk had a scandalous affair with showgirl Josie Mansfield which ultimately broke off when Mansfield took up with Fisk associate Edward Stokes, who then attempted to blackmail Fisk for his illegal doings. Fisk had no part of that, and Stokes killed Fisk in 1872 (and went to prison for 4 years). Fisk was remembered as a populist loathed by high society.

Jay Gould (1836-1892), about the same age as Fisk, but much younger than Drew, was a surveyor and historian, and then formed a tanning business. It was the Panic of 1857 which moved him to high finance, when he bought out his partners’ properties for himself. As with any good, on-the-edge capitalist, this led to some violent kerfuffles, but Gould profited, and soon used his profits to invest in the Rutland & Washington Railroad. He acquired a reputation of being able to move markets by cornering the market in Gold in 1869, culminating in Black Friday, when the price of Gold collapsed. After the Erie War, and then being forced out of that railroad, he acquired the Missouri Pacific, Union Pacific, and Western Union, and transit routes in New York City. among other properties. At one time he held 15% of all US rail mileage. When crushing the 1886 Great Southwest Railroad Strike, he is reported to have said “I can hire one-half of the working class to kill the other half.”

These three: Daniel Drew, one-time partner of Cornelius Vanderbilt, James Fisk, and Jay Gould illegally issued “watered-down” stock in the Erie Railroad, much of which was purchased by Cornelius Vanderbilt who was aiming to get control. Watered-down stock entails the issuing of additional stock in a company, increasing the company’s par value. Suppose a company had issued 10,000 shares of stock initially in exchange for $10,000 of capital. The stock would be watered if the company acquired say $1,000 of additional real assets in exchange for $2,000 in stock. The value of the other stock would in reality be worth less (since the total company assets were now $11,000 but there were 12,000 shares outstanding, each share was only worth $0.91 instead of $1.00. This procedure is no longer done (as such) since par value is now nominal on companies, and the last court case involving watered stock was in 1956.

The more control Vanderbilt wanted, the more stock Drew, Fisk, and Gould issued, costing Vanderbilt $7 million between 1866 and 1868. While much of that was repaid to Vanderbilt, Gould himself could not retain the Erie. This was due to a strange immigrant.

Lord Gordon Gordon

Lord Gordon-Gordon (a.k.a. Lord Glencairn, Hon. Mr. Herbert Hamilton, George Herbert Gordon, George Gordon, George Hubert Smith, and John Herbert Charles Gordon) migrated from Britain to North America in 1870. He was not a Lord, as many Americans and Canadians later learned, merely impersonating a Scottish peer to borrow money to buy land. He landed in Minnesota in 1871, and deposited £20,000 in a local bank, establishing legitimacy. He promised to invest $5 million to help resettle 100 Scottish families on land managed for the Northern Pacific Railroad. Col. Loomis, the land commissioner for the Northern Pacific spent $45,000 touring with Lord Gordon-Gordon through rural Minnesota.

While still leading Minnesota on, Lord Gordon-Gordon, using letters of introduction from Col. Loomis, soon moved to New York. On the train ride east, he befriended the wife of James Fisk. In 1872, he convinced Gould that he and his European friends already owned some 60,000 shares of the Erie RR and he could help Gould acquire control of the Board of Directors of the Erie Railroad, in exchange for $1 million in stock as part of a “pooling of interest.” Upon receiving the stock, Gordon-Gordon promptly sold it, worsening Gould’s position. Gould sued, and Gould’s friends in New York City Hall (then under the reign of their ally and Erie RR fellow Board member, Boss Tweed) had Gordon-Gordon arrested. But Gordon-Gordon made bail based on the reputation of his purported European friends, and promptly fled to Manitoba, before such information could be confirmed, and before his history caught up with him.

“600 shares of Erie, some 1,900 of corporations affiliated with Erie, and 4,722 of the Oil Creek and Allegheny Valley Railroad, twenty-one thousand dollar bonds of the Nyack and Northern Railroad, and $160,000 in currency. The careful recipient of these securities and cash presently found an error of forty thousand dollars in the footing of Gould’s memorandum and sent word of the shortage. Gould did not think there was such an error, but under the circumstances he would not dispute the point and came back with an additional forty thousand dollars in cash. To a modest request for a memorandum receipt, his lordship replied with exceeding dignity that his word of honor ought to be receipt enough, and handed the bundle back to Gould. Gould took it, went as far as the door, returned, laid it down, and departed in faith that his property was in safe hands. It must have been sheer sport in playing a fish which had taken his hook so greedily that led Gordon to demand that Gould separate himself from the old directorate. On March 9 Gould delivered to him his resignation as director and president of the Erie Railroad Company, to take effect upon the appointment of his successor. The great covenant was complete.” (Folwell 1921)

Gordon-Gordon offered to buy large parts of Manitoba from the government, which appealed to locals there, but soon his American enemies found out and sent a posse of bounty-hunters to bring him back to the US. This posse included 2 future Governors of Minnesota and 3 future members of Congress. They successfully kidnapped Gordon-Gordon but were stopped by the Mounties in Winnipeg and put in prison themselves. The Governor of Minnesota put the state militia on alert and President Grant authorized sending an army into Manitoba, and a major international incident between Canada and the US was threatened. To avoid conflict, Canada released the posse, but Gordon-Gordon was already freed. Then his European enemies asked for his extradition on similar charges of swindling a jeweler of £25,000, and Canada agreed. Making his escape again, he was again arrested, and again released on bail. But before his extradition in 1874, he held a party, gave gifts to his local friends, and then shot himself.

Gould’s loss of $1 million in stock may have been sufficient to cost him the Erie Railroad.


Folwell, W. (1921). History of Minnesota, Volume 2. Minnesota Historical Society Press.

Johnston, J. (1950-51). Lord Gordon Gordon. Transactions of the Manitoba Historical Society Series 3.

Adapted from Garrison, W and Levinson, D (2014) The Transportation Experience: Second Edition. Oxford University Press.


Fourth of July 1999 – Stone Arch Bridge |

Cross-posted at Fourth of July 1999 – Stone Arch Bridge

Fourth of July 1999 – Stone Arch Bridge

I had just moved to Minnesota as a new Assistant Professor, and was living in the Marcy-Holmes neighborhood. On the July 4, 1999, I decided to see the fireworks at the nearby Stone Arch Bridge. I went early, enjoyed the warm summer’s afternoon, and slowly the crowd began to fill in this prime spot for fireworks viewing. There were couples, families, people of all ages, races, and stages of inebriation. On one side of me was an immigrant south-Asian family (the women in traditional costume), including a mom and her newborn child. On the other side a fifty-something guy (my guess a native Minnesotan), a bit on drunk side, with his girlfriend or second wife. 
It’s about 8:30 pm, well before the fireworks get going, and the guy thought it would be fun to launch his own rockets off the north/east side of the Bridge. Having seen real fireworks, I never understood the need of people to launch their own, which are mere sparklers in comparison. The first rocket shoots off, makes some sort of pop noise, and there it goes into the water. The second he shoots off and it for some reason boomerangs back to the Bridge, whizzing by (and scraping) me (leaving burn-marks on my shirt) and lands on the blanket the south-Asian mom has laid out. It starts a small fire, which she puts out by beating it with her sandal.Minneapolis's Stone Arch Bridge, Fall 1999

I am pissed, but she is furious, since it missed her baby by inches. The crowd, led by the mom, but including everyone else around starts yelling at the guy, basically asking the rhetorical question “what the hell is wrong with you? Get out.”. He stands there unfazed as a lynch mob begins to form, and he sort of shrugs. The yelling gets louder. His lady whispers to him to the effect that they better leave, and she escorts him off the bridge.

The riot was averted, and the real fireworks proceeded apace. They looked something like this:

I have not returned to fireworks at the Stone Arch Bridge, my preferred location is now Tower Hill, which is not nearly so close to the action, but let’s you see almost every firework display in the Metro area. Unfortunately the Hill is infested with mosquitos and smokers this time of year.


Does TTI underestimate historic congestion levels?

To read the Texas Transportation Institute’s Urban Mobility Report is to believe congestion has more than doubled since 1982 (really between 1982 and 2000). From one perspective, of course congestion must have risen, demand (Vehicle Miles Traveled, Population, etc.) increased significantly over this period while supply (Lane Miles of Road Capacity) did not increase at nearly the same rate.
But I was alive in 1982, I was in cars at that age (and driving myself the next year) (in Central Maryland). I remember congestion in the 1980s. To misquote Lloyd Bentsen, “Congestion was a friend of mine”, and TTI seems to be saying to 1982 “You’re no congestion”. But congestion doesn’t seem appreciably different from today. People complained about it then as much as now. Some bottlenecks have been fixed, new ones have emerged.
So I wonder whether congestion did, in fact, “double”.
Some hypotheses:
1. Measurement issues. Continuous roadway travel time measurements were a lot scarcer in the 1980s than today. Freeways now have loop detectors on every segment, whereas there might have been a permanent recording station every 5 or 10 miles in the 1980s, so a lot more had to be estimated and approximated. There are still no good arterial measurements, the most recent Urban Mobility Report uses GPS data from Inrix, and this will clearly come to dominate congestion measures. Notably, including this measurement forced TTI to re-estimate downward their historical congestion measurements.
2. Definition: As noted by Joe Cortright’s report Driven Apart, mobility is not accessibility. A city where I can reach everything in 10 minutes, but travel at 30 MPH (when freeflow is 60 MPH) is more congested than one where I can reach everything in 30 minutes, but can travel at freeflow conditions. The TTI in a sense penalizes efficient land uses.
3. Induced Demand: Highway expansion tends to get used up (this is not a bad thing of itself, just a thing), so much of road expansion gets eaten up in more traffic. Similarly highway reduction reduces travel. Duranton and Turner write “We conclude that an increased provision of roads or public transit is unlikely to relieve congestion.”
This does not explain why congestion is under-estimated in the past though.
4. Congestion vs. Speed: Travel times on journey to work increased only marginally over this period. Average distances for trips rose faster than travel times, indicating average travel speeds increased. So even with increasing congestion, if travelers shifted to relatively faster (e.g. suburb to suburb freeways) from slower (e.g. suburb to city arterials), congestion can rise on each link, but travel speeds still increase. See The Rational Locator for an example of this.
5. Perspective: This previous point about perception can be refamed as one of perspective. There are differences between spatial averages (which TTI uses) and person-based averages (which individual observers perceive). So the person based average for any metropolitan resident may be the same, but the amount of space (network) covered by congestion may increase if the total amount of space which is developed increases. Similarly, if there is peak spreading, congestion occurs over a longer duration.
However, TTI is not simply saying that the amount of area that is congested increased, they are claiming, for Washington DC the delay per person increased from 20 hours per year in 1982 to 74 hours in 2010.
I am willing to believe that with recent measurements, 74 hours per year for an average commuter in DC is plausible in 2010, since that is just under 10 minutes each way each day for 225 work days per year. 10 minutes of delay on a 30 minute commute means the freeflow time on that commute (un-delayed, e.g. Sunday morning) was 20 minutes. This seems about right for the “average” commuter. Rush hour is when everyone has to slow down.
But this implies in 1982 that delay was less than 3 minutes a day per commuter each way. That seems unreasonably small when you think about it, I could have spent 3 minutes at a traffic light in DC at the time, and that certainly constitutes delay. They are saying for every person who had a 10 minute delay, 2 people had 0 delay to get an average 3 minute delay, and that is not the metropolitan Washington I was familiar with. Congestion was sufficiently important than that radio stations had regular traffic reports, and traffic helicopters, it was not something insignificant.
Of course this is impossible to fully validate, as we cannot go back in time and accurately measure speed. The best I could think of was using the Google NGram feature to track mention of some keywords in books. This proves nothing unfortunately, and suggests a small uptick in the word “traffic” in the 1990s, but is interesting none-the-less.
One however can imagine the motivation for wanting congestion to appear lower in the past than it actually was. This means congestion is rising faster, and thus creates a greater claim on the public weal than if congestion were always with us at roughly the same level.

Going Underground

Prior to the advent of the steam railway, London was a metropolis of just over 1 million people. It was well Figure_c8-f3bFigure_c8-f3cFigure_c8-f3dserved by both canals and turnpikes connecting to other parts of Great Britain. Internally, there were omnibus services. The London & Greenwich Railway was the first of many railways to reach London, with the first section opening in 1836 and being completed in 1838, making it possible to reach Greenwich in twelve minutes instead of the hour required by horse-drawn omnibus or steamboat. Famously built on a viaduct, the route was initially paralleled by a tree-lined boulevard that operated as a toll road, serving those unwilling to pay rail fares. However, the toll road was disbanded when the viaduct was widened to enable more frequent services to the densely populated urban core, ultimately growing from two tracks to eleven.
Soon many other railways sought to connect to London. To avoid disruption in the core, a Royal Commission on Railway Termini, appointed in 1846, drew a box around central London and decreed no line shall enter the cordon. [This box resembles the congestion charging zone adopted in the early 21st century, which aimed to reduce cars, rather than prohibit trains]. The result was railway terminals locating on the edges of the central region. London, like many cities, has no unified railway station, as the North, South, East, and West lines have no common intersection. The problem is worse though in London, as even lines from the north run by different organizations would be build adjacent (St. Pancras/ Kings Cross), or nearly adjacent (Euston), stations without convenient interchange. Later (between 1858-60) some penetrations of the box were permitted by Parliament, but most of the City of London (the original walled city where the financial district still lies) remained untouched. While preventing railways from severing the most densely populated part of the city, which would have been expensive for both the railways and the city, it created a need for a connection between the termini to allow transfers. The Metropolitan Railway, a private concern like all railways of the era but with some support from the Corporation of the City of London, was approved by Parliament in 1854. It aimed to connect the northern termini (Paddington, Euston, St. Pancras, King’s Cross, and Farringdon, which was later added to the plan) to ease movement for through travelers.
The trends in the City of London were quite different from the rest of London. The City of London has seen a long trend of depopulation from 1851 (prior to the first Underground line) and for many years saw increasing employment, lending support to the notion that the railways, especially the Underground, enabled decentralization of residences and concentration of employment.
The Metropolitan Railway opened in January 1863, and was extremely successful. Clearly the market was much larger than inter-line transfers. The firm paid dividends throughout its life. Accounting in the early years of the Metropolitan Railway, especially prior to the Regulation of Railways Act of 1868, was a bit dodgy, and dividends were reportedly paid out of capital. To quote Jackson (1986) p. 38, describing the era of 1865, “It was . . . a house of cards, a precarious game in which the level of dividend was kept up at all costs, by finding money from somewhere, with no regard to sound accounting or financial rectitude.”. Emulation is the proof of success. Many new railway lines were proposed, the 219 London-area railway bills brought before Parliament during the period 1860-1869 totaled 1420 km (882 miles).
Some of those lines were proposed prior to the opening of the Metropolitan, indicating the smell of success was in the air, though the peak years were between 1863 and 1866, following closely on the heels of the Metropolitan’s opening. The most important of these was the Metropolitan District Railway (later called the District line), which ran just north of the River Thames, but south of the Metropolitan, connecting a number of the southern railway termini (Victoria, Charing Cross, Blackfriars, Cannon Street). Proposals for what became the Circle Line service linking the Metropolitan and District (roughly inscribing the box described above) were quickly proposed, but the two lines were not connected on both ends until 1884. Both the Metropolitan and District lines were constructed using cut and cover techniques. Later lines, from the City and South London Railway (first section opened in 1890) onwards, generally used deep-level tunneling techniques to avoid disruption of city streets, existing railway lines, and public utilities when they needed to be below grade. Outside the Circle Line however, the railways could emerge above ground and competed fiercely in some markets, while operating unfettered in others, to provide suburban services. In some cases this involved building new lines, in others it involved acquiring running rights on (or ownership of) existing lines. The development of suburbs was a way to develop traffic for lines that in the city, though profitable, were operating below maximum capacity, and thus maximum profitability.
Adapted from

Also see:

How a chance encounter in St. Paul almost prevented World War II

Cross-posted from How a chance encounter in St. Paul almost prevented World War II :

“While staying in St. Paul, Minnesota, Zeppelin encountered a fellow German who had served for the Union inflating a hot-air balloon. It was here Count Zeppelin first went airborne in 1863. The rest, as the say, is history.”

How a chance encounter in St. Paul almost prevented World War II

The first manned flight may have been in 559, when the Emporer’s son, Yuan Huangtou of Ye, China was forcibly strapped to a kite and set airborne from a tower. Yuan Huangtou was later executed, and this experiment did not lead to any follow-on.

The French Montgolfier Brothers designed and took off in a hot-air balloon in 1783 (with others), which is credited as the first manned free-flight. In 1891, German Otto Lilienthal flew in a glider. By 1898, internal combustion engines were powering airships (dirigibles) designed and flown by Brazilian Alberto Santos-Dumont. Numerous other pioneers made attempts. Two bicycle mechanics, better known as the Wright Brothers then changed the world in 1903.

The history of flight passed briefly through Minnesota on a couple of occasions. Charles Lindbergh grew up near Little Falls, Minnesota. He of course was a leader in the Nazi-sympathizing America First pacifist movement. This was not helpful in the War effort.

However, the relationship of Minnesota and Germany and aviation has another interaction.

Coming to the US as an observer to the American Civil War representing Wurttemberg (Germany was not yet unified), Count Ferdinand von Zeppelin decided to explore the North American frontier (See Botting (2001) for discussion of the history of the Zeppelin Company). While staying in St. Paul, Minnesota, Zeppelin encountered a fellow German who had served for the Union inflating a hot-air balloon. It was here Count Zeppelin first went airborne in 1863. The rest, as the say, is history.

Almost half a century later (1909), the Zeppelin Company he founded was facing financial difficulties selling airships to the German military, and decided to start an airline (DELAG). While it was not at first as successful in organizing regular service, it did provide some (with logistical support from the Hamburg-Amerika steamship lines), marking the first commercial airline.

By 1914, DELAG had made over 2,000 flights, totaling 100,000 miles (160,000 km), carrying 34,028 passengers. World War I changed the nature of airship use, and the German military’s interest. By war’s end, almost 100 airships had been used for the German army and navy, and more than half were lost, indicating lower success than hoped for, and significantly underperforming airplanes. Still, the Americans showed some interest, and after the War, the US Navy ordered some airships from the Zeppelin Company as part of reparations payments, to the anger of some Germans, who disapproved of the technology transfer. An assassin skulked Dr. Hugo Eckener, famous dirigible pilot and the manager of the Zeppelin Company.


Hugo Eckener, Dirigible pilot, Nazi fighterEckener was so prominent in post World War I Germany he almost stood for President against Hitler. But stepped aside when President and war hero Count von Hindenberg chose to run again. Had the anti-Nazi Eckener run (and won of course), he may have proven himself far more competent and avoided the subsequent rise of Hitler altogether.


So St. Paul gave Count Zeppelin his first balloon flight and infected him with the aviation bug. Zeppelin gave Eckener his position with the company and the opportunity to become nationally regarded, and Eckener may have stopped the rise of Hitler.


Prior to the 1938 LZ 129 Hindenberg (named for the Count) disaster in Lakehurst, New Jersey, no passenger had died due to a crash of a Zeppelin airship. Transatlantic Airship travel was not doomed due to this one well-publicized crash, but rather to the rise of Pan American Airways flights, which were much faster, though less comfortable. Though there was an attempt to convert future airships (such as the LZ 130 Graf Zeppelin II) to Helium rather than Hydrogen, the US government withheld Helium supplies under the 1937 Neutrality Act.

Adapted in part from The Transportation Experience, 2nd Edition.


London Underground Stamps and £2 Coin


London Reconnections: In Pictures: London Underground Stamps & £2 Coin :

“Earlier this year, the Post Office confirmed that they would be issuing a number of stamps to commemorate the 150th Anniversary of the opening of the Underground. The designs for these stamps have now been made public, and are featured below. The set features two second class stamps, which focus specifically on the Metropolitan Railway, and four first class stamps taking a broader look at the Underground. In addition, there are four long-format commemorative stamps each of which features a variety of Underground posters.”