Dr. Roget’s description of a new instrument for 
This instrument has been variously modified with a view 
of enlarging its scale, or of adapting it to particular objects, 
such as the calculation of exchanges, the measuring of plane 
and solid bodies, and the computations of trigonometry. The 
Society has recently witnessed its successful application, by 
Dr. Wollaston, to another science, in his synoptic scale of 
chemical equivalents, for the invention of which every prac- 
tical as well as philosophical chemist must acknowledge to 
him their deep obligation. 
But to whatever purposes the sliding-rule may have been 
applied, its use is necessarily limited to those operations which 
are performed by the simple addition or subtraction of loga- 
rithms, and to the corresponding arithmetical operations above 
mentioned. It is not directly adapted to the multiplication or 
division of logarithms by any number, and therefore is not 
directly calculated to perform the involution or evolution of 
numbers, to which, as was before noticed, the multiplication 
and division of logarithms correspond. Yet many practical, 
as well as philosophical, inquiries occur, in which it is neces- 
sary to ascertain the powers and roots of numbers. In all 
researches, for example, which involve geometrical progres- 
sions, or exponential quantities, and whenever the terms of a 
series are to be computed in obtaining approximate solutions, 
these questions present themselves. The common sliding- 
rule furnishes no direct mode of determining even the simple 
power or root of a given number: and when the exponent of 
the required power or root is not an integral, but a fractional 
number, its inadequacy to resolve the question is still more 
apparent. The squares and square roots, it is true, are often 
pointed out on the common rules, by means of a supplemen- 
