3 0 Dr. Roget’s description of a new instrument for 
source, as well as the commodious instrument of discovery 
in every department of mathematical inquiry. The scale of 
Gunter, and the common sliding-rule, are derived from the 
properties of logarithms ; and the purposes to which they are 
immediately applicable are the multiplication and division of 
numbers. The instrument, of which I purpose giving an ac- 
count to the Society in this communication, is founded on a 
particular mode of employing logarithms, and is calculated 
to apply immediately to the involution and evolution of num- 
bers. To those who are already conversant with mathema- 
tical pursuits, a few words would suffice to explain the prin- 
ciple on which it operates : but to such as are not familiar 
with the practical employment of logarithms, or of the com- 
mon sliding-rule, the following statement of the chain of 
reasoning on which they depend, may conduce to render the 
subsequent details more intelligible. 
The mode in which logarithms are instrumental in facili- 
tating computation, is by converting the more difficult and 
laborious into the simpler operations of arithmetic. This is 
effected by substituting, instead of the numbers on which the 
requisite operations are to be performed, other numbers pre- 
viously calculated and arranged in tables, so that every num- 
ber in the natural series, has one of these artificial numbers, 
or logarithms, corresponding to it. These logarithms are 
so calculated, that, by adding together those which corre- 
spond to any given factors, the sum obtained shall be the 
logarithm, or artificial number, corresponding to the product 
of these factors. By consulting the tables, therefore, this 
product may be discovered ; for it will be the number an- 
swering to the logarithm, or sum, thus obtained. The 
