Prof. Young on Algebraic Equations. © 405 
operations and symbols, and arranged in a form so condensed as ra- 
ther to resemble, in appearance, the extraction of the square or cube 
root of a numerical quantity, than the solution of a complete equa- 
tion, but considerably less complicated than even that operation as 
it is generally laid down. All the work is visible to the eye, and is 
arranged in a series of columns beneath the coefficients*: and these, 
step by step, formed by the multiplication of the result in one column 
by a single digit, and added to the next throughout the series, till the 
new subtrahend is found beneath the absolute term. By a repetition 
of the same process, a new trial divisor is found and verified, and the 
coefficient of a new equation, having its roots reduced by the quan- 
tity brought out already, has its coefficients standing in the same 
columns, instead of the original coefficients at the head. A continuance 
of this simple process evolves the root, figure after figure, till the whole 
of them if rational, or as many as are requisite if irrational, are de- 
termined. The process, moreover, instead of becoming more com- 
plicated, and the determination of the next figures more uncertain, 
becomes more simplified in the first respect, and more certain in the 
other; and the last half of the whole number of figures (save one) are 
obtained by mere division. Moreover, it presents at the end of the pro- 
cess, the coefficients of a new equation, which contains the remaining 
roots of the original equation. It thus, whilst the root is actually as- 
signed, presents us with the depressed equation simultaneously pro- 
duced,—an additional advantage of the method. Nor are these all; 
but our space does not allow of our entering into further particulars. 
This substitution of a general method for a general formula is not, 
indeed, the object after which the lovers of mere symbols have been 
straining ; and perhaps such formule, though in their employment, a 
hundred times the work would be required, would be more accordant 
to such prejudices: nevertheless, the mathematician who looks at 
the question with a philosophic eye, will see, that as this process is 
requisite even in the extraction of the roots which any such formule 
must involve, the search after those formule is a matter of mere tri- 
fling. Though it strains at the naked gnat, it can swallow the sym- 
bolized camel,—the more smoothly, the more incumbered it is with 
these useless and unintelligible hieroglyphics! By the mathematician 
who values a result, less by its extreme algebraical complication than 
by the elegant facility of its application to the main purposes for which 
the formule were devised, a method like this must be hailed as one cf 
the greatest boons that has ever been conferred upon the scientific 
community. Its influence will soon be felt in every department of 
philosophy which involves considerations respecting mensurable quan- 
tity, by whatever means the measures can be effected; and in many 
cases even theories will be brought to a decisive test, the numerical 
results upon which this testing depended having been hitherto in- 
volved in equations which no ardour or perseverance could resolve 
by any of the methods heretofore proposed. 
Though this discovery was published in the Philosophical Transac- 
* No letters are introduced, and the whole process is purely numerical, 
