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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 ellipsoid, that is, an ellipsoid of revolution which is flattened at the poles. Degrees of latitude are determined by the angle 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 are the relevant sections. Here is the relevant extract from the Voyage of Hugon. Also, find a brief discussion of Boscovich's example.