Lalande 21185, vis. mag. 7.46, spectrum M2V, distance 8.1 light years, has been photographed at the Sproul Observatory since 1912. Variable proper motion was established by Peter van de Kamp in 1944. Recent studies, preliminary to a definitive least- squares solution, gave a period close to eight years for the photocentric orbit and indicated the necessity for including a secular perspective acceleration term in addition to the proper motion because of the long time interval and the appreciable proper motions of the reference stars. Parallax, proper motion, secular perspective acceleration, and geometric orbital elements were determined by least squares with an IBM 650 computer. The material included 315 nights over the interval 1912 to 1959. Two solutions, using 8.0- and 8.2-year periods, were made; no distinction can be made between them on the basis of the residuals. For further use P=8~.0, T= 1939.9 and e=0.30 were adopted. The combined solution in right ascension and declination yields +0'.'4039~0'.'0021 (p.e.) for the absolute parallax, and 0'.'0336~0'.'0024 for the semi-axis major of the photocentric orbit. Reasonable extremes for the mass of the M 2V star with Mpv = + 10.5 yield the following masses of the unseen companion and the greatest separation ofAand B: MA+MB Am=oo Am=3 1961 MB MB d~ax 0.3000 0.0090 0.0270 0.400 0.011 0.035 0.500 0.013 0.043 It seems unlikely that B could be as bright as Mpv=13.5 (Am =3), have amass as small as 0.0350 (L7268: M~~=15.4; mass=0.040), and have escaped visual detection at a distance of 1". It is concluded that Am >3 and that the mass of the unseen companion is close to 0.010. Assuming the companion to be extremely red some scanning photoelectric device in the infrared, taking advantage of the time of greatest elongation and the position angle might yield the positive results needed for a rigorous mass determination.