164 Theorems for determining 
vessels it readily evaporates at much lower degrees of heat, evett 
at that of the atmosphere. When it is spread thin on a plate 
of glass, if the eye be brought into the same plane the violet 
vapour is discernible at 100°. It evaporates slowly in the open 
air at 50° of Fahrenheit. When put into a phial closed with a 
common cork, the iodine soon disappears: it combines with 
the substance of the cork, tingeing it brownish yellow, and ren- 
dering it friable. 
240 grains of nitric acid, sp. gr. 1°490, saturate 1000 grains of 
the iodic liquid. Sulphurous acid is copiously exhaled as before, 
After filtration a bright golden-coloured liquid is obtained. On 
adding a little manganese to this liquid, iodine sublimes ; but 
the quantity procurable in this way is considerably less than by 
sulphuric acid. 
I am, &ce. 
‘Anderson’s Institution, Glasgow, ANDREW URE, 
August 29, 1817. 
XXV. Theorems for determining the Values of increasing Life 
Annuities, By Mr. J.B. BENWELL. 
To Mr. Tilloch. 
Sin, = d wes followirig collection of theorems embraces an ex~ 
tension of those communicated in a previous Namber of your 
Magazine, being applicable to the valuation of life annuities in- 
creasing by certain orders of a constant numerical ratio. 
The several Life Assurance Companies established in the me- 
tropolis are occasionally in the habit of granting annuities that 
increase by the scale of the natural numbers as well as the mul- 
tiples thereof, and which annuities may be either temporary or 
deferred; but, in respect I (presume) to those institutions which do 
not possess the proper and requisite aids (in conducting this branch 
of scientific research), it has been represented as a matter of much 
apparent doubt, whether the. methods they pursue, in order to 
arrive at the supposed values in these and similar inquiries, be 
rigorously exact and unobjectionable,—.a circumstance that 
imperiously requires elucidation, because it tends to mliitate 
against the avowed professions held out by them, of being guided 
by the pure and unerring principles of mathematical truth. — It’is 
very probable that the practice of granting progressive life an- 
nuities might be rendered almost as general as any other species 
of contingent investment; and what seems chiefly essential to 
the dissemination thereof, is a commodious and accurate formula 
for the solution of the most useful cases. But with the exception 
of one for finding the value of a life annuity, increasing according 
to 
