512 
ME. B. GOMPEETZ ON THE SCIENCE 
order of survivorship ; problems previously considered many years before, and presented 
by my late friend William Morgan, Esq., of the Equitable Society, to the Eoyal Society, 
and published in their valuable Transactions ; and which had been since considered, 
in a learned work on Life Annuities, by my late respected friend Joshua Milne, Esq., 
with some ingenious notation with respect to those contingencies. But still, the 
solutions given to many of the problems, though there were but three lives con- 
cerned, were of such an intricate practical form, as to be in my opinion perfectly 
useless ; especially on considering that it was necessary to obtain, by Tables of single 
and joint lives, by necessary interpolations, the required data; as the differences to 
be used for the interpolations, in consequence of the great irregularity of the numbers 
of those Tables, are so irregular as to throw great doubt on the necessary accuracy 
of the results. And I think the examples I gave of my method could leave no doubt 
as to the comparative simplicity which resulted from it, and consequently comparative 
utility of my analysis ; an analysis which applies where there are more than three lives 
concerned, and, in fact, where there are any number of lives to be considered. And 
I may refer the reader to my solutions in that tract, to enable him to make the com- 
parison. 
There were various other subjects in that paper, and one I mention in particular, 
which is the problem to determine what would be the law of mortality between two 
lives A, B, so that, should it be known that they are both extinct, it would be an equal 
chance which of them had died first ; because that assumption is made, in some of the 
solutions above alluded to, by former writers, and for a short period would, in fact, 
be approximatively true ; and the solution of the problem showed that it could only be 
accurately true where there was for each life a uniform equal decrement, though not 
necessarily the same for both, or else a decrement for each life proceeding in geome- 
trical proportion ; the former law being in fact only an extreme case of the latter law. 
I may mention that there are some omissions in the printed solution of this problem, 
which may lead the reader, if he does not enter properly into the analysis, to think it 
faulty ; and that the paper on the whole stands in need of some errors in the printing of 
it, and in one or two places of an incorrect portion of the manuscript sent to the printer, 
being pointed out. 
Art. 2. Since that paper was written, I ventured to communicate a paper to the Eoyal 
Society, which it did me the honour to print in their Transactions of 1825, as a letter 
to my late friend Francis Baily, Esq., on the nature of the functions expressive of the 
law of human mortality expressed by the equation ; where L^, according to 
my notation in my first paper, is the number of persons living, at the age out of the 
number Lo who were born x years previously. And as I use, from great preference, the 
fluxional notation of our great Newton, instead of the furtive notation used on the Con- 
tment and now much used in England, my d does not denote the differential character. 
I say I use the notation in preference, because I consider the fluxional calculus far more 
luminous. But as strictures have been cast on me on that account by some readers of 
my paper, I will not apologize for a small digression from my subject, to state some 
