452 
PliOFESSOK K. PEAPtSOX ON MATHEMATICAL 
Tims: (71 = 25 - 88401 , (/o = 11 - 77326 . 
Hence by (xxiv.) a = 8 - 268 , 405 , 
and by (xxv.) log iJq = 24 - 275 , 3032 . 
We have accordingly for the equation to the curve : 
{x - 8-268, 405 )ii ''326 
y = lO'^- X 1-884,965 
25-88401 
The distance from the origin to the mean is given by the first equation of (xxii.): 
/r/ = 16-98913, 
or, the theoretical range starts with brides of 5’198,570 + 8-268,405 = 13-466,975 
years. This is an excellent underlimit to tlie age of women marrying men of 24 to 
25 in a country like Italy. Our first group is at 15-5, and the above start is just two 
base units before this initial group. 
The skewness = '498,953, and the distance from mode to mean = 1-822,004, or 
the mode is at 20-3657 years. 
Turning now to Type V. we have the following results :— 
16//3i = 8-249,262. 
Hence Equation (xii.) is : 
[p _ 4)2 _ 8-249,262 (p - 4) - 8'249,262 = 0. 
Thus the positive value of p is : 
p = 13-150,747. 
Equation (xiii.) gives : 
y= 129-73081. 
Then (xiv.) gives : 
log ?/q = 22-367,6952. 
Thus the equation to the curve is : 
y — 10^2 X 2-331,821 03-13-150,747 e-139-730Sl/.._ 
To find the position of its start we have by (xv.) : 
jXy = 11 -6343, 
or, since the mean age of brides is 22-1877, the youngest possible theoretical bride is 
10-5534 years. This is probably a worse determination of the underlimit than in the 
case of Type VI. At the same time I notice that out of about 180,000 women, 101 
