The onset of longitudinal vortices in horizontal Blasius flow isothermally heated from below is studied analytically. The assumption that at the onset of thermal instability the thermal disturbances are confined within the thermal boundary layer is employed for the limiting case of large Prandtl number. Polynomial representations for the basic quantities obtained by the integral method of the boundary layer analysis have been used. Then the system of differential equations and boundary conditions for disturbance quantities is reformulated in a convenient form so that the solutions may be constructed as rapidly convergent power series. The critical buoyancy parameter G $r_{x}$ $^{*}$ /R $e^{*1.5}$ falls between 2 and 6, which is about one order of magnitude lower than the existing experimental values. It is also shown that the positions of the onset of instability can be closely predicted by the present theory.y.y.