Given that hexagons are growing on average for each period, negative values generally represent lower relative growths than hexagons with positive values in Figure 8. As an example in the initial period (1822–1825), there is a trend of greater relative growth of geolocated addresses in the city center compared to the periphery, indicating a notable center-periphery gradient.

Some periods may be marked by general decline. This is particularly true of the years 1900–1904, where the average slope is -0.222. The positive values of the hexagons thus reflect a lower relative decline than those of the negative values (in strong decline). The decline in the number of geolocated addresses[7] is fairly widespread throughout Paris, although some areas are still growing[8]: south-west, north around Montmartre and the Nord and Est railway stations, and east in the 12th and 20th arrondissements.

The general decline in 1900–1904 reflects editorial choices made by the company that published directories during this period. Indeed, starting from 1903, the editors of the Didot-Bottin initiated the creation of a separate directory dedicated to prominent individuals, titled the Bottin mondain [Firmin-Didot and Firmin-Didot 1903]. This new edition led to the exclusion of individuals from the Didot-Bottin general directory studied here. The excluded entries are varied, notably individuals designated as owners or annuitants, but also deputies, ministers, or advisors at the Court of Cassation. Other categories such as bankers, placement agents, and doctors remained in the general directory. Thus, these people were not considered to belong to this social echelon by the editors of the time, and/or they were deemed indispensable to the list of actors in the socio-economic life of Paris, appearing in both lists (the specific Bottin mondain list and the general list).

The socio-spatial divide of Paris from west to east is well-known during the 20th century, notably thanks to historical studies of the Bottin mondain conducted by Cyril Grange [Grange 1993]. However, the gradient of the social division of Parisian space at the turn of the 20th century is clearly identifiable on the 1900-1904 map in Figure 8. The gradient is not entirely linear. It includes a hyper-concentration (dark green hexagons on map) of prominent inhabitants in the 8th arrondissement (south of Parc Monceau) and the 16th arrondissement (Chaillot neighborhood). On the other hand, a continuum of affluent neighborhoods is apparent in the city’s center-north (9th arrondissement), center-southwest (in the 7th arrondissement between Saint-Germain and the Invalides), and in the center near the Saint-Louis Island. Other areas are also noteworthy, in particular the Petit Montrouge district in the south of Paris in the 14th arrondissement. Indeed, the south of the district is wealthy (see Appendix 8.4), whereas the concentration of affluent families is almost invisible on the scale of the districts of Paris studied by [Grange 1993]. This is likely due to the fact that his study is based on a sample of 4,500 addresses from the Bottin mondain between 1903 and 1987, i.e. a sampled view of one social group (that of the Bottin mondain), whereas the present study is based on all the addresses of the directories, i.e. an exhaustive view of a set of social groups (of the directories).

Figure 8 lets us analyze the density trajectory of a city segment over time. The data-driven approach offers two main advantages: 1) We do not predetermine the study area a priori, e.g. by selecting districts or arrondissements; 2) the dynamics of the area under study are examined in relation to the urban space as a whole.

In the 1850s and 1860s, the west of Paris underwent significant street development, leading to the emergence of new neighborhoods and increased urban density in these areas. Indeed, while only 9.3% of Haussmann’s construction expenditure was associated with the newly annexed area beyond the Fermiers généraux, most of the work was carried out in western Paris, with the development of the Place de l’Étoile and the Champs-Élysées, for example [Faure 2004]. Street development is well-documented in cartographic sources [Andriveau-Goujon 1868] and particularly significant in the 16th arrondissement and the south of the 17th arrondissement, south of the railroad lines leading to the freight station near Batignolles and the Saint-Lazare station (see Figure 3). However, the rate and extent of the densification of this area are unknown.

This area has been entirely covered by hexagons since the mid-1850s (in particular beyond the Fermiers généraux wall, see Figure 8). Geolocated addresses show overall positive slopes from that point until 1900, but the normalized slopes per period shown in Figure 8 only exhibit consistently positive trends from the mid-1880s in the 16th arrondissement (with the exception of the years 1864–1870). On the other hand, they show positive trends from the mid-1850s onward for the southern part of the 17th arrondissement (except for the period 1880–1885). Consequently, compared to other parts of Paris that experienced densification during the second half of the 19th century, the intensity of densification in the southern part of the 17th arrondissement was significant enough by 1855–1860 to be notable on a citywide scale. However, it was not until another three decades later that densification in the 16th arrondissement became apparent, coinciding with a period of deceleration in densification across the city.

Several factors contribute to understanding this difference in the pace of densification in Paris. Firstly, large industrial establishments were set up mainly in the north and east of Paris between 1850 and 1870. This partly accompanied the urban growth and densification shown in Figure 8. Subsequently, Haussmann’s work in central Paris involved the construction of new streets and the reorganization of city blocks to accommodate new buildings. To achieve this, the administration’s authority to expropriate property was extended in 1852. Between the end of that year and 1859, 2,236 houses were demolished by expropriation in Paris, according to Haussmann himself. As a result, over time, some of the city’s inhabitants migrated to more peripheral areas — notably to the east — all the more so as rents of older constructions raised dramatically in the 1850s (by over 50%). Lastly, the newly built-up areas of the north of the 16th and south of 17th arrondissements are characterized by wide avenues and a high concentration of Haussman-style buildings, which have a low built density compared to other Parisian areas [Larroque and Jigaudon 1980] [Faure 2004].

In addition, qualitative analysis of the geocoding quality of directory entries in the years 1855–1860 reinforces the identification of the local trajectories of the south of the 17th arrondissement. Figure 3 shows geocoding problems in the western edge of the city. In 1855, some entries were incorrectly geocoded, as in Jouffroy street, south of the railroad lines. All the addresses in the directory refer to the “Passage Jouffroy,” opened in 1845 and located in Montmartre. The densification dynamic between 1845 and 1850 observed by the two pink hexagons in Figure 8 is thus a geocoding bias. On the other hand, the problem of distinguishing between the Jouffroy passageway and street during geocoding is the same for the years 1855 and 1860. Consequently, the calculation of space-normalized slope for this period — and subsequent periods — is not altered by this geocoding bias, and the growth of the southern 17th arrondissement since 1855–1860 is historically dynamic.

Large-scale city maps are one of the most valuable detailed topographic sources for building cartographic representations of past urban landscapes. Once georeferenced, they act as a geographical proxy, locating entities such as streets, buildings, and addresses on the surface of the Earth. In order to leverage historical maps as a geocoding basis for the city directories, we gathered a gazetteer of address points and streets created within previous digitization initiatives.

The resulting gazetteer contains around 136,500 geographic entities digitized from four maps and atlases of Paris (Figure 9). 94% are address points with their number and street name; the remaining 6% are named streets, approximated by their halfway point. Each geographic entity is anchored temporally by a time interval corresponding to the survey period of the source map, or to the publishing date if the survey period is unknown. Thus, the information of the gazetteer is time-dependent. Figure 9 represents the gazetteer and its entities clustered in time according to the production periods of the four maps and atlases. Each depicts Paris at different phases of its morphological evolution: on the eve of the Revolution for the Verniquet atlas, in the 1830s after the phase of national property subdivision for the Jacoubet atlas, before the Second French Empire for the Andriveau-Goujon map, and after the major Haussmanian transformations for the Municipal atlas.

The atlases focus on the area within the administrative boundaries of Paris, i.e. within the Fermiers généraux limits before 1860, and Thiers wall after that date. However, numbering inside the administrative limits is only partial. In the Jacoubet atlas for example, the zone between the boulevards and the Fermiers généraux wall is mostly urbanized, yet address points are very sparse. We are faced here with the discrepancies of these cartographic sources, which combine multiple, heterogeneous administrative sources, possibly partially out of sync with the exact historic reality of urbanization. In addition, the suburbs of Paris prior to 1860 are not included in the current state of the gazetteer.

All addresses identified in the directory entries are automatically geocoded. For this purpose, the open-source geocoding software Pelias[14] has been adapted to make it time-sensitive. The geocoder is built around the ElasticSearch indexing and search engine[15]. It is an adaptation of [Cura et al. 2018] for ElasticSearch to improve the performance and accuracy of the process. We refer to this paper for the methodological and technical details on spatio-temporal geocoding.

A “spatio-temporal” geocoding query consists of the name of the address to be located, a geographical level (street or address point) and a target date. The geocoder searches for potential candidates within the gazetteer and orders them by combining the similarity of their address name with the query and a time distance value between the query date and the temporality assigned to the gazetteer entity.

Parisian directories are commercial editions, involving competition between publishers, buy-outs over time and moments of editorial monopoly. We revealed five main periods thanks to the inventory of directories [Baciocchi and Cristofoli 2022]. The years 1780–1793 are those of the origins. It was followed by the emergence of the Almanach du commerce (1798–1815). Competition was fierce, and publications abounded until 1856, when the Firmin-Didot brothers bought the Bottin publishing company. Thereafter, the period 1857–1890 was characterized by the hegemony of the Didot-Bottin collection, before a new period of competition began in 1891 and lasted until 1914.

The number of copies produced by editors grew through time. It shows how directories were received and the importance of the enterprise: La Tynna published 4,500 copies in 1816; Bottin 9,000 in 1840; Firmin-Didot brothers 18,000 in 1857, and 45,000 in 1878. The latter wrote in their 1857 introduction: “to judge the importance of such a publication by a single material fact, one need only say that, for the eighteen thousand copies printed, almost all of which are sold with binding, it is necessary, because of the size of the volume, for a flock of several thousand sheep to provide their hides each year for this bookbinding” [Firmin-Didot and Firmin-Didot 1857, p. 8, our translation].

At the beginning of the 19th century, alphabetical lists included prominent inhabitants, while professional lists featured merchants. In 1817, editor La Tynna alphabetically listed merchants but maintained a separate alphabetical address list for each population. Consequently, the alphabetical lists used for the study are not comparable in terms of social coverage before and after the end of the 1810s. We could incorporate the professional lists spanning from 1787 to 1816 in our sub-corpus to extend the temporal scope of the study. However, we have recently extracted the data for these lists and have chosen to focus solely on the alphabetical lists, of which we have a more comprehensive understanding.

The publisher Bottin merged both alphabetical lists (merchants and prominent inhabitants). We wish to begin the study period in 1820, one year after Bottin’s first publication and the first year for which we have a digitized version. However, at that date, the alphabetical list of merchants in the Bottin directory contained a system of cross-references to the pages of the list by profession. During the NER phase, page references were identified as street numbers, generating noise during the geocoding phase. Consequently, we have decided to start the study period in 1822, when Bottin’s cross-referencing system was no longer in use.

High-quality digital versions of directories are not consistently available. For instance, the year 1830 lacks a suitable digital version, prompting us to select the 1829 Bottin directory instead [Cristofoli and Baciocci 2024]. Additionally, we wish to study identical collections over time whenever possible, as their content is more uniform compared to different series and collections. For example, we have access to the Didot-Bottin collection from 1860 onward and we have chosen the year 1909 instead of 1910. Indeed, there is no high-quality digital version for the 1910 Didot-Bottin directory, whereas one is available for 1909 and yet a processed version of the 1910 Paris-Hachette directory.

A list of ten directory entries in “rue Sainte-Croix-de-la-Bretonnerie” (Figure 10, top table and map, \(e = 10\)), selected from the Didot 1845 directory, helps to explain the definitions used in the paper and the following indicators.

The named entity recognition (NER) processing shows that these 10 entries contain 8 addresses (\(a = 8\)), defined as character strings combining address.name and address.number. Indeed, the address of “Rousselle, pharmac. en chef au Val-de-Grâce” does not exist in the original source and a NER detection problem had truncated the original entry “George, bonneterie et nouveautés, Rochechouart, 10 [4]”. An address is geolocated if the geocoding process is able to match the character string of the address with the gazetteer (i.e. when geocoding.has_geocoding is true). In this example, 7 addresses are geolocated with the Jacoubet atlas (\(ga = 7\)), and “Baril-lerie, 7” was not found in the gazetteer.

The “distinct addresses” of a directory, shown in the second table in Figure 10, refer to all the unique character strings tagged as addresses by the NER (\(da = 6\)). Two strings that are close but slightly dissimilar are considered as different addresses whenever a small variation appears, as in the case of “Ste-Croix-de-la-Bretonnerie, 54” and “Ste-Croix-Bretonnerie, 54”.

Finally, the distinct geolocated addresses refer to unique point geometries associated with the directory entries (see section 4.1 for an extended definition). Here, in the bottom table of Figure 10, 4 distinct geolocated addresses had been found (\(dga = 4\)).

The evaluation of the geocoding process for each of the directories is presented in Figure 11. Three main points stand out in the table.

Firstly, the ratio of the number of addresses per number of entries is always greater than 1 (see \(a/e\) in Figure 11), and mainly between 1.05 and 1.2, because individuals can have an activity at several addresses. Two typical cases exist: On one hand, the directory lists the place of manufacture and the place of sale of an individual, or the various store units of an individual; on the other hand, a store has two addresses because it is located at a crossroad and its storefront faces two streets.

Secondly, the geocoding of addresses is systematically higher than 89.1% – as shown with ratio \(ga/a\). On average 95.7% of addresses are geocoded, varying from 89.1% to 98.2%.

Thirdly, the geocoding of distinct addresses is very good. Indeed, the ratio of distinct geolocated addresses per distinct addresses is between 0.966 and 0.99 (see \(dga/da\) in Figure 11).

There is no cartographic source of addresses in the gazetteer for areas outside the Fermiers généraux wall before the 1860 extension of Paris. Entries located outside the Fermiers généraux wall in the 1845 directory are therefore mostly geolocated with the 1888 Municipal atlas. However, the urban fabric of Parisian edges between the pre- and post-1860 underwent dramatic changes, and the geocoding is less accurate here than in the city center.

A meticulous manual study of the addresses geolocated in these areas in 1845 reveals various problems in the outcome of the SoDUCo automated pipeline chain (Figure 12 and 13).

Leaving aside complete failures of the geocoding processing caused here by a myriad of peculiar forms in the addresses extracted from the directories, three typical borderline cases can be identified and summarized:

• Erroneous NER. Bad geolocations are linked to poor or imperfect recognition of entities by the NER. This is easily identifiable when the address text is made up of weird character strings or irrelevant words. But it can be more difficult to detect when the false-address is plausible enough to be associated with an address in the gazetteer. The geocoder provides a procedure for excluding some identifiable cases (custom_catchall_alwaysvalid in Figure 12), but incorrect parsing raises the question of how to handle complex address descriptions, which can sometimes be fragmented into several directory addresses.
• Incorrect street name in the directory. In few cases, the directory itself provides incorrect information, which has an impact on the geocoding processing (mainly spelling mistakes and typos).
• Street absent in the gazetteer. Sometimes the gazetteer is incomplete or inaccurate. Some streets, attested by their frequency of appearance in a directory, are not present in the gazetteer (e.g. Napoléon quay). In other cases, streets are present but without numbers. In this case, the geocoding process may favor another gazetteer offering addresses, even if the temporal consistency loses quality.