586 
CHEMISTRY: G. N. LEWIS 
imaginary parts of the function or the series. In particular the series 
2^^-^ cos {an log n + 2(97rw) (p >0) (5.1) 
is never convergent or summahle for any value of 6, and is accordingly not 
a Fourier^s series. We thus obtain a solution of what, in our former 
paper, we call Fatou's^ problem which combines all the advantages 
of those given previously by Lusin,^ Steinhaus,^ and ourselves. 
We can also obtain in this manner exceedingly elegant examples of 
continuous non-differentiable functions. Thus the function 
f W = V 5inif!li2gJl±^ (l</3^f) (5.2) 
does not possess a finite differential coefficient for any value of 6. 
^ G. H. Hardy and J. E. Littlewood, Some problems of Diophantine approximation ■ 
(i) Proc. Fifth Int. Congress Math., Cambridge, 1, 223-229 (1912); (ii) Acta Math., 37, 155- 
190 (1914); (iii) Ibid., 193-238. 
2 G. H. Hardy, On certain oscillating series. Quarterly J. Math., 38, 269-288 (1907). 
3 G. H. Hardy, Weierstrass's non-differentiable function, Trans. Amer. Math. Soc, 17, 
301-325, (1916). 
c. supra (1) {in), p. 225. 
^ G. N. Watson, The singularities of functions defined by Taylor's series. Quarterly J. 
Math., 42, 41-53 (1911). 
^ G. H. Hardy: (i) A theorem concerning Taylor's series, Ibid., 44, 147-160 (1913); (ii) 
Note in addition to a theorem on Taylor's series, Ibid., 45, 77-84 (1914). 
^ Cf. E, Landau, Abschatzung der Koeffizientensumme einer Potenzreihe: (i) Arch. Math. 
Physik, ser. 3, 21, 42-50 (1913); (ii) Ibid., 250-255; (iii) Ibid., 24, 250-260 (1915). 
^ E. Landau, Uber die Anzahl der Gitterpunkte in gewissen Bereichen, Gottinger Nach- 
richten, 687-771 (p. 707), (1912). 
^ For references see p. 232 of our paper (1) (iii). 
STERIC HINDRANCE AND THE EXISTENCE OF ODD 
MOLECULES (FREE RADICALS) 
By Gilbert N. Lewis 
CHEMICAL LABORATORY, UNIVERSITY OF CALIFORNIA 
Received by the Academy, September 6, 1916 
The discovery of certain unpredicted facts in organic chemistry has 
led to the employment of the elusive phrase 'steric hindrance/ a phrase, 
however, which seems too vague in its significance to connote a real 
scientific theory. If a steric influence upon a chemical reaction be 
defined as one which is due to the room occupied by a large atom or 
group of atoms, such a definition leaves an opportunity for that kind of 
confusion, which is too frequently found in chemical literature, between 
