1064 é 
deflection @ remains a small fraction of a radian. Seeing that in the 
experiments the angles reach a value of .07 the condition was 
obviously not satisfied, at least not to a degree sufficient to guarantee 
a sufficient accuracy of the results; in that case it would have been 
necessary to go down to amplitudes as much as a hundred times 
smaller. However this is only a rough estimate which does not exclude 
the possibility of the accuracy having after all been higher than 
was to be expected on the above ground, seeing that no account is 
taken of the numerical factors the value of which can only be given 
by a further approximation in the theoretical treatment of the 
problem’). For this reason it seemed desirable to make a further 
investigation into the dependence of d on the amplitude: this investi- 
1) Comp. G. ZEMPLÉN, Ann. d. Physik, 38, 84, 1912. 
The condition given in the text only holds moreover in the limiting case, where 
the time of oscillation is very small. In that case we have (see Comm. N’. 1480, § 17) 
dw 
R? 
wo = wR —etr-R) where 6b = a is a large number, and thus —- ——bw 
r? 7 Or 
0? dw 0 
and =—b = b?w, from which it follows, that is small as compared 
0? 0? ees 
to =a and rien n= 7? so that the term 3E actually gives the order 
of magnitude of the terms of the first order. If on the other hand the oscillatory 
movemement is very slow (b very small; see Comm. 148), § 18), we have 
tay R® R® -7’ oat A TE Sh RE 12. 28 eva 
= R RER" ence Or? 7 — a Or oa Re Es Rh?’ 
de 
D , : 
practically disappears ; in that case w” must be small 
dt 
whereas the term with 
0° 
with respect to dn ‚ and we thus obtain, except for a numerical factor, the 
u Or 
same condition as given by LAMB and RayreiGH (LAMB. Hydrodynamics, 1906, 
uk 2 
p. 547) for a uniform rotation viz. wr R < BE symbol << standing for: much 
smaller than). Whereas for very rapid oscillations the condition was a << 1, 
12 aT RES 
27 ph? Rh? = RY 
indefinitely with increasing T. In the general case (bh neither specially large, nor 
very slow oscillations require a << and this limit can rise 
00 Ow u dw 
De aR aT OE 
doubtedly a much more complicated condition holds, probably expressing, that 2 
must be very small as compared to a number which depends on the value of 
DR and, as far as | have been able to ascertain, is larger the smaller the value 
of DR, i.e. the larger 4, J and T' and the smaller u and R (comp. Comm. 1488, - 
equation 20). 
are of the same order and un- 
specially small) the three terms 
