Abstract or Summary 
 This history concerns the scientific contributions of Charles
Babbage (17911871) to mathematics, to the invention of calculating
machines, and machine tools, to the development of scientific ideas
through a wide variety of scientific investigations and his involvement
in several different scientific reforms. Babbage considered himself
a philosopher in the broadest sense of the word and looked upon the
whole of science as his domain of inquiry. The broad speculative
and philosophical aspects of his scientific inquiries; the theoretical
and technical aspects of his work relating to mathematics and calculating machines; and his ideas concerning the development of science
as a profession and the role of government in the support of science
will be examined in relation to his scientific career. Babbage began his scientific career in 1812, when, as an
undergraduate at the University of Cambridge, he joined with John
Herschel (17921871), Edward Ffrench Bromhead (17891855), George
Peacock (17911858), and other students to form the Analytical
Society for the purpose of promoting the study of mathematical analysis
and introducing the methods and notation of the differential calculus
of Gottfried Wilhelm Leibniz (16461716) to replace the fluxional
calculus of Isaac Newton (16421716). Babbage and his friends were
actually carrying out a reform movement begun by Robert Woodhouse
(17731827), a professor at Cambridge, whose ideas had not gained
much acceptance until the Analytical Society was formed. The members
of the Society published mathematical works which utilized
Leibnizian methods and notation; translated and supplemented an
elementary calculus textbook by Sylvestre Franiois Lacroix (1765
1843), a French mathematician; wrote and published three books of
examples to accompany Lacroix's textbook; and gained control of the
mathematical content at Cambridge by becoming moderators of the
annual Senate House examinations and posing examination questions
which made use of Leibnizian methods and notation. Through these
activities the members of the Analytical Society were successful in
achieving their mathematical reform by about 1822.
Babbage and his associates continued to promote scientific
reform throughout the eighteen twenties and thirties by attempting, unsuccessfully, two reforms in 1828 and 1830 of the Royal Society; by
successfully reforming the Nautical Almanac and Astronomical
Ephemeris which prior to 1811 had been the foremost work of its kind
in Europe; and by forming new scientific societies. After Babbage and
his associates were unsuccessful in attempting the reform of the Royal
Society in 1830, David Brewster (17811839), a scientist and Vice
Chancellor of the University of Edinburgh, assumed the leadership for
the group and founded the British Association for the Advancement of
Science in 1831. Babbage participated in the British Association
between 1832, when he was named a permanent trustee, and 1839 when
he resigned because of an intrigue by another trustee of the Association.
These reform activities and his mathematical researches form
the first aspect of Babbage's career, between about 1812 and 1840.
Babbage established a reputation as a firstrate mathematician through
his work in the calculus of functions, in statistics, and in probability
theory. As the result of his mathematical work, he was named
Lucasian Professor of Mathematics, a chair which Newton had held
and which Babbage held from 1828 to 1839. Babbage was also instrumental
in the founding of a statistical section of the British Association
in 1833. In 1834, the statistical section was established as a separate
society, the London Statistical Society, and it was in this Society that
Babbage remained active for the remainder of his life. A second aspect of Babbagets scientific career began about 1820
and was devoted to the development of automatic calculating machines.
His first calculating machine, Difference Engine No. 1, was designed
to calculate and print mathematical and astronomical tables. Babbage
received a gold medal from the Astronomical Society of London in
1823 for the invention of Difference Engine No. 1. He worked upon
this engine from 1823 to 1833, during which time he received support
from the government. After 1833, following a dispute with his
engineer, Joseph Clement, Babbage ceased work upon Difference
Engine No. 1 and began work upon a new calculating engine, the
Analytical Engine. Babbage continued to negotiate with the government
concerning Difference Engine No. 1 until 1842, when the government
formally withdrew its support of the engine.
Babbage continued to work upon the Analytical Engine for the
remainder of his life. This machine employed many of the features of
modern digital computerspunched cards for data and instructions;
an arithmeticallogical unit; a unit to store instructions, data, and
results; and a printing device for recording the results of the calculations.
In 1848, Babbage also drew up plans for a Difference Engine
No. 2 based upon the improvements resulting from the development of
the Analytical Engine. While none of the calculating machines were
completed, the principles upon which they were based were fully
demonstrated by the portion of Difference Engine No. 1 which was assembled in 1833; by the advancement of the machine tool industry
and mechanical,engineering through the development of new machine
tools, new standards of tolerances and mechanical drawings, and a
mechanical notation; and by the advanced principles employed in the
Analytical Engine which was capable of calculating any function and
was therefore an entirely general calculating machine.
In addition to his reform activities, mathematical researches,
and work with calculating engines, Babbage carried out many varied
scientific experiments which were reported in publications throughout
his career. Although he is remembered primarily for his work as a
reformer and as an inventor of calculating machines, Babbage
possessed broad interests and an inquiring intellect as demonstrated
by such diverse publications as a book on life assurance societies, a
paper on his invention of occulting signal lights for lighthouses, a
paper on his experiments with magnetism, and a paper on the principles
of turning and planing metals.
