# 1700-1799: New graphic forms

The 18th century witnessed, and participated in, the initial germination of the seeds of visualization which had been planted earlier. Map-makers began to try to show more than just geographical position on a map. As a results, new graphic forms (isolines and contours) were invented, and thematic mapping of physical quantities took root. Towards the end of this century, we see the first attempts at the thematic mapping of geologic, economic, and medical data.

Abstract graphs, and graphs of functions were introduced, along with the early beginnings of statistical theory (measurement error) and systematic collection of empirical data. As other (economic and political) data began to be collected, some novel visual forms were invented to portray them, so the data could "speak to the eyes".

As well, several technological innovations provided necessary nutrients. These facilitated the reproduction of data images (color printing, lithography), and other developments eased the task of creating them. Yet, most of these new graphic forms appeared in publications with limited circulation, unlikely to attract wide attention.

Contour maps showing curves of equal value (an isogonic map, lines of equal magnetic declination for the world, possibly the first contour map of a data-based variable)

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Halley:1701 Abbott:1884First test of statistical significance based on deviation between observed data and a null hypothesis (used to show that the guiding hand of a devine being could be discerned in the nearly constant ratio of male to female births in London over 1629--1710)

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Bellhouse:1989 Arbuthnot:1710Literal line graph, inspired by observation of nature (section of hyperbola, formed by capillary action of colored water between two glass plates)

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Hauksbee:1712Experiments paving the way to the development of photography: Images obtained by action of light on a mixture of chalk, nitric acid, and silver salts

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noneThe normal distribution, derived as the limit of the binomial distribution

The normal distribution was first introduced by de Moivre in an article in 1733 (reprinted in the second edition of his The Doctrine of Chances, 1738). Laplacelater extended this in his book Analytical Theory of Probabilities.A further generalization, to the central limit theorem occurred later.

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deMoivre:1733 deMoivre:1738 Laplace:1812Development of the use of polar coordinates for the representation of functions. Newton's Method of Fluxions was written about 1671, but not published until 1736. Jacob Bernoulli published a derivation of the idea in 1691 attributes the development of polar coordinates to Fontana, with no date.

1671 is probably too early; 1736--1755 would probably be more appropriate. There are earlier references to Hipparchus (190-120BC) regarding the use of polar coordinates in establishing stellar positions, and Abu Arrayhan Muhammad ibn Ahmad al-Biruni (1021) regarding the use of three rectangular coordinates to establish a point in space.

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Smith:1925First use of the term "statistik.'' The word "statistics'' was first used by Zimmerman in 1787. (For the earlier use of "statist'', "statista'' and other terms, see cite{John:1883}.)

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Achenwall:1748 Zimmerman:1787 Walker:1929Beginnings of the estimation of $m$ unknown quantities from $n$ emipirical equations (where $n > m$), taking account of the possibility of errors in the observations (later supplanted by the method of least squares)

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Mayer:1750 MarieBoscovich:1755 Farebrother:1999Introduction of a notation which gives a name and address to every possible point in 3D space, $(x,y,z)$.

To find the true place of the body at each instant, one only needs to locate it at the same time in respect to the three fixed planes, each perpendicular to the others[p. 89].

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Euler:1752"Carte chronologique'': An annotated timeline of history (from Creation) on a 54-foot scroll, including names and descriptive events, grouped thematically, with symbols denoting character (martyr, tyrant, heretic, noble, upright, etc.) and profession (painter, theologian, musician, monk, etc.)

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Ferguson:1991 Wainer:1998Diagrams developed to represent color systems. In 1758, Mayer developed a system of constructing and naming many of the possible colours. Lambert extended this with a 3D pyramid indicating "depth'' (saturation).

Lambert wanted to extend the coverage of the system to include the concept of depth. He believed that the colour pyramid would be useful to textile merchants to decide if they stocked all the colours, and to dyers and printers as a source of inspiration.

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Mayer:1758 Harris:1766 Lambert:1772Theory of measurement error as deviations from regular graphed line. (Lambert made the observation that "a diagram does incomparably better service here than a table.''cite[p. 204]{Tilling:1975}

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Lambert:1765Historical timeline (life spans of 2,000 famous people, 1200 B.C. to 1750 A.D.), quantitative comparison by means of bars

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Priestley:1765Repeated systematic application of graphical analysis (line graphs applied to empirical measurements)

Lambert was one of the first to use graphs to analyze experimental data, and to use graphical calculation, e.g., computing the slopes of curves to estimate rates of change.

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noneDevelopment of descriptive geometry, that leads to engineering drawing

Monge's work, Descriptive geometry, was the first consciously formulated exposition of the science of orthographic projection and descriptive geometry. Sylvestre Lacriux discovered the principles of projection independently about the same time as Monge. Jean Pierre Hackette added new material to Monge's descriptive geometry and published a book on this subject in 1822.

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Taton:1950 Taton:1951Graphical analysis of periodic variation (in soil temperature), and the first semi-graphic display combining tabular and graphical formats

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Lambert:1779 Hankins:1999Statistical map of production in Europe, possibly the first economic and thematic map (shows geographic distribution of 56 commodities produced in Europe)

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Crome:1782Use of geometric, proportional figures (squares) to compare demographic quantities by superposition, an early "tableau graphique''

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Palsky:1996 Fourcroy:1782Visualization of vibration patterns (by spreading a uniform layer of sand on a disk, and observing displacement when vibration is applied)

Chladni is known as the father of acoustics; he also invented the euphonium.

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Chladni:1787Patenting and sale of printed graph paper, printed with a rectangular coordinate grid, attests to the growing use of Cartesian coordinates

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noneMulti-number graphical calculation (proto-nomogram: contours applied to multiplication table, later rectified by Lalanne cite{Lalanne:1846})

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Pouchet:1795Automatic recording of bivariate data (pressure vs. volume in steam engine) "Watt Indicator,'' (invention kept secret until 1822)

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noneInvention of lithographic technique for printing of maps and diagrams ("At the time the effect of lithography ... was as great as has been the introduction [of the Xerox machine]'' cite[p. 57]{Robinson:1982}) (published in several translations, 1818--19)

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Abbott:1884First maps of the incidence of disease (yellow fever), using dots and circles to show individual occurrences in waterfront areas of New York