3i 6 Mr. hellins’s Theorems 
ley, in the Philofophical Tranfadtions, N° 216, and of 
which the dodtor faid, it converges fo very fail, that, in 
his opinion, nothing better was to be hoped. 
There are yet fome contrivances different from thofe 
mentioned in the beginning of sherwin’s book of ma- 
thematical tables, or any other that have come to my 
hands, whereby the labour of computing a table of loga- 
rithms is fhortened ; but to explain them would require 
more time than my prefent fituation affords me. 
The obfervations and reafonings which led me to the 
difcovery of the above theorems, I imagine, need not here 
be mentioned. Such as they are, I beg leave to lay them 
before the candid and fkilful in thefe matters, in hopes 
that the invention will appear to them, as it does to me, 
a ufeful one. 
It has, indeed, been objected, by a gentleman of my 
acquaintance, that improvements in the conftrudtion of 
logarithms cannot now be ufeful, becaufe logarithms are 
already conftrudted. 
4 
I anfwer, that argument, if it has any weight, ope- 
rates equally againft Sir Isaac newton, Dr. halley, 
Mr. cotes, Mr. simpson, and feveral other ingenious 
mathematicians; for logarithms were invented, and 
tables of them conftrudted, before their time ; fo that if 
I fhould be thought to have mifemployed my time in 
improving 
