Ishiwara showed that this new hypothesis can be used to reproduce some quantum effects known at that time. Thus, he succeeded in obtaining an expression for the quantization of the angular momentum in the Bohr atom, taking into account also the ellipticity of electron orbits, although it followed from his theory the need to take the charge of the nucleus of the hydrogen atom equal to two elementary charges. As a second application of the proposed hypothesis, Ishiwara considered the problem of the photoelectric effect, obtaining a linear relationship between the electron energy and the radiation frequency in accordance with the Einstein formula. Later in the same year Ishiwara put forward another hypothesis, according to which the product of the energy of the atom and the period of electron motion in the stationary state should be equal to the integer number of Planck constants. In 1918, he linked the postulate proposed three years earlier to the theory of adiabatic invariants. Around the same time, analogous rules for quantizing systems of many degrees of freedom were independently obtained by William Wilson and Sommerfeld and are usually called the Sommerfeld quantum conditions. The reason for the error of Ishiwara, which was manifested in the calculation of the hydrogen atom, apparently was a superfluous averaging over the number of degrees of freedom (dividing by formula_1 before the sum). At the same time, his quantum condition, which differed from Sommerfeld's one in the presence of summation, allowed to obtain correct results regardless of the choice of coordinates. This was pointed out in 1917 by Einstein, who, not knowing about the work of the Japanese colleague, derived the same relation and showed that in the case of separable coordinates it gives the conditions of Wilson and Sommerfeld.