1. (1) The science reports of the Tôhoku Imperial University, 11 (1922) 43-50. Cf. the simple proof of Prof. Kakeya this journal. 1 131-133.
2. (2) We assume that this inequality holds from r=0, but it is easily seen that the final result is true, when we only assume that the inequality holds for r≥r0.
3. (3) E. Borel. LeÇons sur les fonctions entières. p. 63.
4. (4) When ρ=0, evidently limn=∞logn/logrn=0.
5. (5) We find the inequality (8) in Okada's original paper. l. c. 49. We have assumed an not to be zero, but when an is zero, the inequality (8) evidently holds.