A M_s 7.7 earthquake struck the western, equatorial coast of Sumatra in December 1935. It was the largest event in the region since the two devastating giant earthquakes of 1833 and 1861. Historical seismograms of this event from several observatories around the world provide precious information that constrains the source parameters of the earthquake. To more precisely quantify the location, geometry, and mechanism of the 1935 event and to estimate the coseismic deformation, we analyze the best of the available teleseismic historical seismograms by comparing systematically the records of the 1935 earthquake with those of a smaller event that occurred in the same region in 1984. First we constrain the source parameters of the 1984 event using teleseismic records. Then, we compare the records of the 1935 event with those of 1984 from the same sites and instruments. To do this, we choose several time windows in the corresponding seismograms that contain clearly identifiable phases and deconvolve the modern event from the older one. The deconvolutions result in very narrow pulses with similar sizes, thus confirming similar locations and mechanisms for the events. The initiation of the 1984 event was on the subduction interface at a depth of 27 ± 2 km; its M_0 is 6.5 x 10^(19) N m (M_w is 7.2). The sense of slip was nearly pure thrust, on a plane dipping 12°. The 1935 event also involved rupture of the shallow subduction interface, but was about five times larger (M_0 3.3 x 10;^(20) N m, M_w 7.7) and initiated a few kilometers to the southeast, along strike. The 1935 rupture propagated unilaterally toward the southeast. The along-strike rupture length was about 65 km. From these source parameters, we calculate the surface deformations, assuming an elastic multilayered medium. These deformations compare favorably with those actually recovered from paleoseismic data in the form of coral microatolls
