16 Dr. Roget’s description of a new instrument for 
A 
a logarithm answering to the number 1.4294, the product 
we have been seeking. But this product is itself a logarithm, 
namely, the logarithm of the power required. The number 
having for its logarithm 1.4294, namely, 26.878, is therefore 
the power sought for, or 2.123 4 ' 3719 . 
It may be observed, in this last example, that of the num- 
bers added together, the first was the logometric logarithm, 
(that is, the logarithm of the logarithm) of the given root: 
the second was the simple logarithm of the exponent ; and 
the sum of these was the logometric logarithm of the power. 
If, therefore, we were at the pains to construct a table having 
three sets of columns ; the first containing the natural series 
of numbers; the second, their corresponding logarithms; and 
the third, containing the logarithms of those logarithms ; we 
should possess the means of raising any given number to any 
given power, by the simple addition of the numbers in the 
second and third columns ; just as common multiplications 
are effected by the addition of common logarithms. It is evi- 
dent that a line might be graduated so that its divisions should 
correspond to the numbers in the third column, or should 
represent the logometric logarithms of the numbers marked 
upon them: and if this line were applied so as to slide against 
another line logometrically divided, it would enable us to effect 
the very operation I have been describing, and thus give us, 
by inspection, the powers corresponding to any given root 
and exponent. 
The instrument, then, in its simplest form, W'ould consist 
of tw ? o graduated scales applied to each other. A portion of 
these scales is represented, PL II, fig. 1. The lower rule, 
AA, which I shall call the slider, is the common Gunter’s 
