Extant paper records of the early analog seismic network of Taiwan represent a large resource for earthquake studies in several disciplines. In this study, we report on T waves generated from offshore earthquakes, based on analog observations. The T phases were identified from their stable apparent velocity of about 1.5 km s^-1 and other observations using data recorded by stations in eastern Taiwan and on two nearby islands. The observed T phases are recorded for the first time from Taiwan, and in particular are observed by the network in the distal range of local earthquakes. Most of the T waves are observed at island stations at epicentral distances greater than 100 km. For earthquakes that occurred a great distance east of Taiwan, the T phases are always the most dominant phases observed at island stations east of Taiwan, and are also seen at some inland stations with smaller amplitudes. No T phases from inland events were observed by stations on Taiwan or on nearby islands. The observations indicate that the amplitude of the T phase is highly attenuated on its land path and that the propagation direction of the T phase is affected by water depth.