NORMAL VARIABILITY 93 
These values are plotted in the accompanying 
diagram (Fig. 6) as vertical distances above a base 
line. The figure obtained by joining together the 
points thus arrived at may be observed to show some 
resemblance to the previous Figs. 4 and 5. 
The three series of numbers already given are those 
which: are obtained on expanding the expressions 
(I+1)%, (I+1)3, (t+1)*. In general the probabilities 
of the various possible combinations when » coins are 
tossed simultaneously are given by the expanded value 
of (r+1)*. 
Quetelet has worked out the relative probabilities of 
the most frequent combinations in the case of 999 coins 
simultaneously tossed—.e., the expanded value of 
(r+1). A few of these values are given in the . 
following table ; 
TABLE III. 
Heads. Tails. Preatilty. 
500 499 ro 
501 498 0°996 
502 497 0'988 
503 496 0°976 
504 495 o'961 
505 494 0°942 
510 489 0803 
520 479 0°432 
530 469 _ 0155 
540 459 0'037 
550 449 0'006 
560 439 0°0006 
It may thus be seen that the likelihood that a result 
appearing in any given throw will show a still greater 
