Roger Joseph Boscovich
b. 18 May 1711, Ragusa (Dubrovnik),
Croatia
d. 13 February 1787, Milan, Italy
Roger Boscovich (Rugjer Josip Bošković) was educated by the
Jesuits at the Collegium Ragusinum
(College of Ragusa) and at the Collegium
Romanum (College of Rome). He himself joined the order. Under
the employ of Pope Benedict XIV he and the English Jesuit Chrisopher
Maire (1697-1767) surveyed the area of the Papal States during the
years 1750 to 1752.
The Earth has the shape of an oblate spheroid, that is, an ellipsoid
of revolution which is flattened at the poles. Degrees of latitude are
determined by the angle that a normal to the idealized surface of the earth
makes with north. Consequently a degree of latitude near the equator is
smaller than a degree near a pole. Various measurements had been made
of the length of arcs of meridians at this time in Europe and other
parts of the world.. As part of his studies, Boscovich assessed
the available data to estimate the ellipticity of the Earth. In
the adjustment for errors Boscovich used the method of least
absolute deviations.
In 1755, an account of the survey by Maire and Boscovich was published
as De
Litteraria Expeditione per Pontificiam Ditionem ad dimetiendos duos
meeridiani gradus. A translation of
this work was made by Fr. Hugon in 1770 under the title Voyage
astronomique et geographique, dans L'etat de L'Eglise.
A memoir by Boscovich summarizing the account was published in 1757
under the same title De
Litteraria Expeditione per Pontificiam Ditionem in De Bononiensi scientiarum et artium
instituto atque academia commentarii 4, pp. 353-396.
Finally, we note a poem by Benedict Stay (1714-1801), his Philosophiae Recentioris
published in 1760 to which Boscovich wrote notes. In Tome
II is found how he fit equations to data.
Hugon's French translation included the more recent data on the length
of arcs of meridians and also a supplement drawn from the notes
Boscovich wrote for Stay's poem. The
unit of length in these measures is the toise, about 6.4 feet. The
versed sine (versine A = 1 - cos A) appears in these computations in
order to avoid squaring the sine function. That is, 1- cos 2A = 2sin2
A = versine 2A. Here is the relevant extract from the Voyage of Hugon. Also, find a
brief discussion of Boscovich's
example.