G. MOKANT 
329 
And doubtless a, could be found in a similar if more complicated form ; but 
such expressions do not suggest any great hope of our being able to derive /3 and 
in from the mean and standard deviations of the intervals occurring in jJcriods T. 
In the same way the equations for the mean Tif and the standard deviation a, 
of the array of n's for values of t fi'om ^ to ^ + dt do not look very likely to lead any- 
where in the case of a finite ^, i.e. 
(T-t-n/3r 
Ht = r-TTTZ (XXXI), 
1 I m"+i(7i-l)! 
0"t n + "r = : — TTTT (XXXll). 
mn+i (n- 1) !j 
(iii) All these results, however, admit of comparatively easy development when 
there is no " closed-time " /3. 
In this case for the frequency distribution of N intervals 
N{T-tr 
m"+' (H - 1)! , .... 
.tn,t^- r~7^ ^ (xxxiii) 
1 + e'" P - 1 
x'(T-tr 
, say. 
We have already seen what in, and cr, ,j are. We will now find v, and cr„ 
1 \m 111" {n - 1) !j ~ i ( {n - 1) ! in"-' 
Or, Nt = ,~ dte~~^*, 
vv 
^ 1 1) !] 
iiv- \\{n- -2)\ m''''] III' I 1)1 m''-'] 
, e ™ + ^ e >" (It. 
nv VI- 
This shows us that the frequency curve for intervals t is 
T-t 
— c '" 
, ..... 
(.XXXUl)'"". 
l+e'" - -1 
If we make T infinite, tliis reduces to the well-known form )/ = —c "'. We have determined its mean 
m 
and standard deviation in the text. 
