C 71 ] 
found would be preferable to the other 5 as will be 
fhewn hereafter. 
That there are fuch intervals, Dr. Halley’ s tables 
of obfervations fufficiently fhew 5 for inftance ; out 
of 302 perfons of 54 years of age, there remain, 
after 16 years (that is, of the age of 70) but 142 
the decrements from year to year having been con- 
ftantly io; and the fame thing happens in other in- 
tervals j and it is to be prefumed, that the like would 
happen in any other good tables of obfervations. 
Bur, in order to fhew, in fome meafure, the ufe 
of the preceding theorem, it is neceflary to add 
another problem ; which, tho’ its folution is to be 
met with in the firft edition of my book of annui- 
ties on lives, yet it is convenient to have it infertecl 
here, on account of the connexion that the appli- 
cation of the preceding problem has with it. 
In the mean time, it will be proper to know. 
What part of the yearly rent fhould be paid to the 
heirs of the late poffeffor of an annuity , as ntay 
be exactly proportioned to the time elapfed between 
that of the lajl payment , and the very moment of 
the life’s expiring . To determine this, put A for 
the yearly rent 5 L for the part of the year intercepted 
between the time of the laft payment, and the in- 
flant of the life's failing ; r the amount of 1 /. at 
the year’s end: then will ~~l A> be the fum to 
r — 1 
be paid. 
Pro 
