[ 6 23 ] 
mountain, that had been forming within it for fome 
years, and was rife n above the fidcs i and throwing 
up, by violent explofions, immmfe quantities of 
ftones, lava, afhes, and fire. At night the flames 
burft out with greater vehemence, the explofions 
were more frequent and horrible, and our houfes 
fhook continually. Many fled to Naples, and the 
bolded perfons trembled. For my own part, I re- 
folved to abide the event here at Fortici on account 
of my family, confiding of eight children, and a 
very weak and aged mother, whofe life muff have 
been loft by a removal in fuch circumffances, and 
fo rigorous a feafon. But it pleafed God to preferve 
us; for the mountain having vented itfelf that night 
and the fucceeding day, is fince become calm, and 
throws out only a few allies. 
LXXXV. A further Attempt to facilitate 
the Refolution of Ifoperimetrical Problems . 
By Mr. Thomas Simpfon, F. R. S. 
Read April 1 3. BOUT three years ago I had the ho- 
nour to lay before the Royal Society 
the inveifigation of a general rule for the refolution of 
ifoperimetrical problems of that kind, wherein one, 
only, of the two indeterminate quantities enters along 
with the fluxions, into the equations exprefling the 
conditions of the problem. Under which kind are 
included the determination of the greateff figures un- 
der given bounds, lines of the fwifteff defcent, folids 
3 of 
