On the vibrating motion of unevenly thick strings
According to Jacobi, a treatise with this title was read to the Berlin Academy on February 21, 1760. According to St. Petersburg Academy records, it was presented to that Academy on December 1, 1760.
Euler presents his explicit solution of the initial value problem for a string made up of two uniform parts of different densities. Since the differential condition of continuous slope at the junction is not always satisfied, he replaces it by an integral condition that has the differential condition as a special case. (Based on Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances.)
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 9, pp. 246-304.
Opera Omnia Citation
Series 2, Volume 10, pp.293-343.