The determination of the distance of a given point on ground by measuring the lenght of one side and two angles of a triangle formed by that point and two other known reference points
(Szepesolaszi, March 25th, 1795 – Buda, April 8th, 1846)
One of the most remarkable figures of Hungarian water-engineering, he elaborated, among others, the plans of the Vaskapu (Iron Gate on river Danube)-regulation and the river Tisza-regulation.
He obtained a diploma in engineering in 1816 in the Institute of Engineering (Institutum Geometricum) organised at the university of Pest.
For a few years he was engaged in the hydrographic cartographic work of the river Tisza and the Körös rivers, then he was ordered to take part in the surveys of the Danube. On the basis of his hydrographic experience gained at the Körös rivers and the Danube he published two essays (Introductio in praxim triangulationis and Auflösung einiger wichtigen Aufgaben als Beitrag zum geometrischen Triangulieren) in the first one he gave useful advise to cartographic engineers how to determine the first-order points of reference and second-order points of reference when making a net of triangulation with a simpler procedure than the calculating methods used until then, providing a network of smaller than 5-10 thousand km2. The Auflösung... is the direct continuation of the previous study in German illustrating by geometrical examples and mathematical demonstration the methods.
In 1829, as a shipping engineer of the Lower Danube, he was commissioned to lead the surveys of the Danube. In 1833-1834 he accompanied István Széchenyi on his study-trip to England, and after he was engaged in the greatest environmental transformation brought about through river control projects and moor drainage in the 19th century. First on the basis of the plans of István Széchenyi and Pál Vásárhelyi, the Danube was made navigable to the Black Sea between 1834-1896.
Then Vásárhelyi, as the first shipping engineer of the Water Management and Architecture Administration, became one of the most important state leaders of traffic-oriented river regulations.
He took part actively in elaborating the plans of the regulation of the river Rába and its influent rivers, and he was also engaged in the regulation of the Budapest stretch of the Danube and in theoretical problems, for example the determination of the mean flow rate of a river. He was the first one in Hungary to prove that the distribution of speed values in a given perpendicular of a river can be described with a parabola with a horizontal axis.
In 1843 he made one of his most important work titled Esetmérési Térképe Magyarországnak... az Adriatenger víztükrére alkalmazva..., (approx. Land surveying Map of Hungary... related to the level of Adriatic) in which he performed the determination of the height above sea level of the Danube and its affluent rivers and recorded the data on the Lipszky's map of Hungary. He connected the levelling surveys made until then in individual and relative systems and related them to the level of the Adriatic Sea. Defining the basis level of the country the real altitudes could be determined. The levelling project was directed by Vásárhelyi.
In the early 1840's Vásárhelyi was commissioned to make the water regulation plans of the Upper-Tisza region which was stricken by floods the most, and he finished them by 1845.
Between 1846 and 1880, the winding Tisza was shortened by 452 kms (40 % of the original length) by cutting through 36 meandering turns along which many hundreds kilometre long dykes were built.
On the basis of them he was commissioned to make a Tisza-regulation plan. By 1846 he had prepared this comprehensive regulation concept presently known as Vásárhelyi's Tisza-regulation plan.
Memberships: Corresponding (1833) and full (1840) member of the Hungarian Academy of Sciences.