684 
If the two points of discontinuity «= .«#, and «=u, are very 
near each other, they may appear as a single accumulation in the 
rough frequency-curve. 
l The former (simplified) analysis then 
required a very steep slope in the curve 
z—f(«) at this- point, by which the 
smooth character of the curve is often 
disturbed (fig. 184). 
b 
Eje 3 . 8 
SE Xe Considering however this accumulation 
Fie.18 a. Fie.18b. as a fusion of two discontinuities, we 
may assume that the function is three-valued in the immediate 
vicinity of « = es (fig. 185) Usually the smooth transition may be 
obtained by freehand drawing. Care must however be taken that 
the three-valued zone remains as 
narrow as possible. 
The reaction-curve must now be 
modified in such a way that in the 
point 6 the reaction becomes neither 
very small and positive, nor zero, 
c 
b 
Fico. 19a. Fis. 19 b. 
but negative. 
So instead of the shape of fig. 19a the reaction-curve obtains the 
shape of fig. 195. 
Astronomy. — “Calculation of Dates in the Babylonian Tables of 
Planets”. By Dr. A. PANNEKOEK. (Communicated by E. F. van 
DE SANDE BAKHUYZEN). 
(Communicated in the meeting of September 30, 1916). 
By the researches of F. X. Kverer S. J. in Valkenburg we have 
for some years been acquainted with the methods and results of 
Babylonian astronomy during the period of its highest development. 
The material for this was provided by a number of more or less 
damaged fragments of clay tablets covered with cuneiform writing, 
which are preserved in the British Museum, and which have been 
very carefully copied by Srrassmaigr. They contain observations and 
calculations made in advance of the places of the moon and planets 
from the 5 centuries before the Christian Era, the complete deci- 
phering and explanation of which is given by Kucrer in his work 
“Die babylonische Mondrechnung” (1902) and in Vol. I of his 
larger work “Sternkunde und Sterndienst in Babel” (1907). 
