314 
On Jiandom Occurrences in Space and Time 
the distribution excluding the first group are found about "5, using abruptness 
coefficients. These are transferred to t = 0, giving 
/^/' = 2-929,7114, n," = 14-781,9089, 
which give il/i and M.. respectively. Using these values the first approximations to 
/3 and m (i.e. /3„ and m„) are, by equations (iv) and (v), 
m„ = 2-429,7114, /So = "428,8488. 
Then the first and second moment coefficients of the first group about t = 0 
(ft]' and fx./) are given the values they would have for and and these are, by 
(vi) and (vii), 
fi,' = -464,2481, fM^' - -215,9042, 
leading to Ci = 2-858,5599, c, = 14-361,5450, 
and finally by (viii) and (ix) the second approximations to and m. 
If it be thought necessary, these values can be used to redetermine /x/ and jj^' 
and hence third approximations to /3 and in. The results were in our case : 
/3 ni 
2nd approximations -370,552, 2-488,007, 
3rd approximations -368,867, 2-488,841. 
The second approximations would be quite sufficiently accurate for most 
purposes. 
N 
The areas of the curve y = — e corresponding to the observed frequencies 
can be easily found when m and /3 are known. 
The usual test of goodness of fit* gave a veiy low value for P and it was 
clear that this was largely due to the very bad agreement of the first two groups 
(Table I). Clubbing these together (i.e. taking the first group from yS to 1-5) gave 
the much higher value P = '222. It seemed possible that this disagreement at the 
beginning of the range might be due to the fact that too few observations had been 
included in the first group and to test this the material was regrouped on the 
bases to 1, 1 to 2 etc. This arrangement gave the constants 
/3 m 
2nd approximations -362,918, 2-495,527, 
the intermediate steps being 
= 3-390,0644, yu/' = 17-848,5430, 
m, = 2-390,0644, /3„ ='468,3801, 
fi; =-724,3450, fiJ =-548,1725, 
Ci =2-858,4446, c, = 14-398,3602. 
Even without a knowledge of the probable errors of ^ and m we can safely say 
that the differences between these values and those found for the other grouping 
* Tables for Statisticians and Biometricians, Table XII. 
