1887 .] Mr T. B. Sprague on a Fruitful Marriage. 
343 
A study of the results thus far obtained, satisfied me that 
the most satisfactory course would he to arrange my facts 
into two classes, the first relating to those men who married as 
peer or heir-apparent, and the second to those who did not. 
For business purposes, we of course prefer to err, if at all, on the 
side of safety ; for instance, in calculating the risk attaching to 
an insurance against the birth of issue, to take the probability of 
issue rather above than below the truth, and thus to make use of 
that body of facts which gives the smallest probability of failure 
of issue. 
In order to increase the number of the facts, especially at the 
higher ages, I have thought it desirable to take into account, as 
far as practicable, those marriages of the fathers and grandfathers 
of peers, from which the peers were not descended. There were, in 
all, 110 fathers and grandfathers who were more than once married. 
In the case of 61, the peer was descended from the first marriage, 
and in the remaining 49 from the second marriage. As already 
mentioned, these 61 first marriages, of course, have to be excluded. 
We must also exclude the 49 first marriages, corresponding to the 
49 second marriages from which the peers were descended ; for it 
is obvious that these 49 marriages will include an unduly large 
number of cases where there was either no issue or no male issue. 
We have thus to reject all the first marriages; and, of the second 
marriages, we can only make use of the 61 that correspond to the 
61 first marriages from which the peers were descended. We have 
also 13 third marriages, and one fourth marriage, making in all 75 
marriages of fathers and grandfathers, to be taken account of. In 
62 of these, the man married when he was peer or heir-apparent ; 
and in 13, he did not so marry. 
Collecting our results, we now obtain the figures in the following 
tables G and H, where it will be observed that, at each decennial 
group of ages, the percentage of childless marriages is considerably 
greater among those who did not marry as peer or heir-apparent, 
than among those who did. 
In order that our results may be practically useful for professional 
purposes, as, for instance, in the calculation of the values of the 
interests of the various heirs in disentail proceedings, it is necessary 
to graduate the probabilities. This I have done by the graphic 
