G. MORANT 
313 
In finding these values should first be found with great accuracy, re- 
membering the difticulties with regard to even the first moment of curves with a 
finite initial ordinate and an abrupt departure from that ordinate. AL must be 
found with the same accuracy. 
Now Hi being the observed number in the first group and /a/, /h^' its first and 
second moment coefficients about ^ = 0; /x/', /jio" the first and second moment 
coefficients of the remainder, (N — Hi) about ^ = 0, we have 
NCi = Hiyu/ + (N — Hy) /U./', 
NC.2 = tlifl^' + {N - yU„", 
whence Cj and Cg will be determinable from the observations : for /a/ and fj..^ are to 
be given the values they would have for ^„ and and {N — n^) /u,/' and (N — n^) /jl^' 
are and ilf, respectively. 
Let fix be the theor-etical frequency in the range i = /So to 7, then 
■n,= \ — e dt = N{l-e , 
h„mo \ ) 
fy AT JL±L^ { JyjzM) 
n,/x,'=\ — e tdt = N\/3o+ m, - (7 + m„) e \ , 
n, /x/ - —e "'<' t'dt = N \ {/3„ + »i„f + - [(7 + m^f + ■?«„-] e 
_ ( y - M 
Thus ^1 = (TT^ (vi), 
1 -e~ 
( y - g.) 
, _ (^1, + ?»o)- + ?/to'' - {(7 + rn„)- + ??io-| e .. 
I - e 
Now knowing Cj and from the observations in this way, we have from the 
whole theoretical curve Cj = /3 + m and c, = (/3 + mf + 7/i'-, and accordingly 
= c, — Ci'-^ or m= sJci — c-^ (viii), 
/3 = Ci — m or /3 = — Vc, — Cf (ix). 
These give the second approximations to /3 and m, and if necessary we can use 
these values to redetermine /a/ and fx.,' and proceed to a third approximation. 
We will now illustrate the process on the experimental data for the frequency 
of intervals in an indefinitely long time. The smallest interval recorded was 
•39 sec, and it seemed that /3 was fluctuating slightly throughout the experiment. 
To make the influence of the first group as small as possible, 7 was taken to be "5 
so that the first group would be from /3 to 'S and succeeding ones, "5 to 15, 
1"5 to 2 5 and so on. To find /3 and m, the first and second moment coefficients of 
