##

# Johann Heinrich
Lambert

b. 28 August 1728

d. 25 September 1777, Berlin

O.B. Sheynin has given in the Archive
for the History of the Exact Sciences Vol. 7, pp. 246- 256 a
summary of Lambert's
work on probability. This he divides into three parts: theory of
probability, demographical statitistics, and theory of errors. His
outline is followed below.

## Theory of Probability

In "Examen d'une espece de superstition ramenée au calcul des
probabilités" published in Nouveau
Mémoires Acad. Roy.
Sci. et Belles Lettres Berlin 1771 (1773) he consideres
derangements.
This is the game of Treize or Rencontre studied by Nicolas Bernoulli, Moivre, Euler
and Laplace.

His thoughts on subjective probability may be found in the Neues Organon (1764) Band
I and Band
II. In the former is "Alethiologie oder Lehre von der Wahrheit,"
pages 453-592 and in the latter is "Phänomenologie oder Lehre von
dem Schein," pages 217-435. That is, these are the "Theory of the
Truth" and the "Theory of Appearance."

Published in the Opera mathematica
of J. H. Lambert is "Mathematische
Ergötzungen über die
Glücksspiele." This appeared in 1799 long after his death and
consists of three notes on games of chance: the card game known as the
lottery, dicing and heads & tails.

## Demographics

Lambert studies mortality, life expectancy, duration of marriages
among other related topics in "Anmerkungen über die Sterblichkeit,
Todtenlisten, Geburthen und Ehen." found in Theil
3 1772 pp. 476-569. See also his correspondence in Lamberts deutscher Gelehrter Briefwechsel
Bd
4 pp 365-368.

Daniel Bernoulli also
studied the duration of marriages.

## Theory of Errors

The Photometria, sive, De mensura
et gradibus luminis, colorum et umbrae (1760) : Parts
I and II, Parts
III, IV and V, Parts
VI and VII is the primary
source for understanding Lambert's theory of errors. An English
translation by David L. DiLaura is available as
Photometry, or, On the measure and
gradations of light, colors, and shade (2001). The relevant sections
are 271-306.

We find also in "Anmerkungen
und Zus tze zur practischen Geometrie," Part I,
pp. 1-313 of the
Beyträge zum Gebrauche der
Mathematik und deren Anwendung I,
a discussion of the errors. This is followed later by "Theorie
der Zuverlässigkeit der Beobachtungen und Versuche" pp. 424-487.
Additional sources: See also
the site
maintained by Maarten Bullynck of the works of Lambert.