CONNECTED WITH MOETALITY. 
541 
of them which may die ; and the other problem, to assure the like sum on the death 
of A in particular, provided it happens in the lifetime of B. 
Then if A and B were of equal age, and both subject to the same law of mortality, 
without any speciality, the value of the assurance in the first case would be just double 
of that in the second case, for however long or however short the assurance might be. 
But if A and B were both sailors, continually together in the same ship, the common 
risk for each by risk of shipwreck, &c. would equally attach to each ; and if the 
assurance were only for a few hours, say, for instance, for one voyage from Dover to 
Calais, so that the risk for time were insignificant with respect to the common unin- 
fluenced risk ; there then would be only to be considered the risk for each not to escape 
the consequence of the wreck ; but the chances would now come into play, of all on board 
being lost, of none being lost, or of a portion, and what portion of them being lost ; and 
that the portion lost were the two A and B, or only one of them, and which one that 
might be, which might depend on the powers of each for swimming ; but should the 
chance be that the wreck, if it happened, would cause the death of both A and B, then 
the assurance for the period of the intended voyage on the death of one of them only, 
of both, or of one in particular named, of this in the lifetime of the other, would be all 
the same. This is but one case of specialities, and specialities of influences of risks. 
And perhaps there are very few cases of assurances and valuations connected with con- 
joint lives, if any, or even of single, with reference to affections which may arise from 
climate, localities, epidemics, endemics, ancestorial influences, &c., and also epochs, which 
are not affected by speciality ; but though the subject may be very interesting, I have 
not in this paper entered largely on it, but will only now touch on a portion of it which 
may be found by my readers well worthy of their attention. Suppose by the common 
law of mortality, uninfluenced by any speciality, out of the number of the age a, repre- 
sented by L„, there would be living in x years the number ; but that they each for 
any period become subject to an extra risk of death during an infinitely small time, 
t=ccx, where a may, as the case may be, be either a constant quantity or a function of x ; 
then it is evident Jj^+x will not be the number of them living in x years ; and to find 
what that number would be, suppose it represented by ; then its fluxion M^, on the 
supposition that the lives of the then existing number were not deteriorated by the 
pre-existence of those specialities to that period, would evidently be 
But it is to be observed that this supposition is not necessarily tenable, but it would be 
so in case the circumstance of speciality was transient after the moment of its opera- 
tion ; such, for instance, if it were a wreck at sea, leaving no effects ; and therefore I 
shall at present only consider the case when the hypothesis is tenable. And resuming 
the equation, we have 
