Geoscience Reference
In-Depth Information
reflector to concentrate the light into the right direction along the arm of the triangle.
This had an advantage because at night the atmosphere over such long distances
was settled more than during the heat of the day. The images were clearer, refraction
of the rays in air of different densities was less confusing, and the angles could be
measured more accurately.
Snell's techniques were demonstrated by relatively small-scale projects by him and
other Dutch cartographers. The first survey by triangulation is regarded to be Snell's
survey prior to 1615 of the Netherlands from Alkmaar via Amsterdam, Leiden, Utrecht,
Dordrecht and Breda to Bergen-op-Zoom, accumulating an overall distance of 120 km.
This revealed the considerable demands, not just for the survey and the measurements,
but also for subsequent calculations. Not until the invention of the decimal point in
arithmetic notation and of logarithms to replace long multiplication and division by
addition and subtraction
8
,
as well as the invention of accurate instruments to measure
angles, was it practical to make a large-scale cartographic survey of an entire country.
The Academy and Picard took up Colbert's challenge with enthusiasm, using
instruments which Picard had made and which were the most accurate of the time.
Picard set out to survey a line, on the same scale as Snell's, from Malvoisine, a country
building southeast of Montlhéry 30 km south of Paris, to Sourdon, 20 km south of
Amiens, in total a distance of some 150 km along the north-south line through Paris.
PICARD'S FIRST TASK as he began in 1668 was to lay and measure a fundamen-
tal baseline on an arc of the meridian. The baseline ran from Villejuif, just south of
Paris, to Juvisy, 11 km further south, across the flat plain near Fontainebleau (right
across what is now Paris's Orly airport). Picard determined its orientation astro-
nomically by observing star positions and laid it accurately north-south.
To measure the length of the fundamental baseline, Picard used wooden rods at
the standard length of 1 toise
9
. Two assistants were each given a one-toise measur-
ing rod and five pegs. Starting at the first surveyor's stake, the first rod was laid on
8
The first person to use a decimal point to separate the whole number part from the decimal part was
the Edinburgh mathematician, John Napier, Laird of Merchiston in Scotland, in a topic called
Mirifici logarithmorum canonis description
(1614), where he also explained his invention of loga-
rithms (other contenders for the title of inventor of logarithms include the Swiss mathematician Jobst
Burgi, who was credited as such by no less an authority than Johannes Kepler): “Seeing there is
nothing (right well-beloved Students of the Mathematics) that is so troublesome to mathematical
practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square
and cubical extractions of great numbers, which besides the tedious expense of time are for the most
part subject to many slippery errors, I began therefore to consider in my mind by what certain and
ready art I might remove those hindrances. And having thought upon many things to this purpose,
I found at length some excellent brief rules to be treated of (perhaps) hereafter. But amongst all, none
more profitable than this which together with the hard and tedious multiplications, divisions, and
extractions of roots, doth also cast away from the work itself even the very numbers themselves that
are to be multiplied, divided and resolved into roots, and putteth other numbers in their place which
perform as much as they can do, only by addition and subtraction, division by two or division by
three.” The techniques produced workable tables of logarithms from 1624.
9
A
toise
was the French unit of length before the meter, and was about 5 centimeters short of two
meters long.
