Page:Lectures on Ten British Physicists of the Nineteenth Century.djvu/107

sions requires a good deal of "justification" on the part of the compositor. To avoid this expense and the loss of space Stokes introduced the linear notation a/b and dy/dx. The symbol: and ÷ likewise indicate division but he did not use them in the text. He did not use / in writing out centered equations, excepting where it is needed to simplify the index of an exponential function. He considered it convenient to enact that the solidus shall as far as possible take the place of the horizontal bar for which it stands and accordingly that the quantities immediately preceding and following shall be welded into one, the welding action to be arrested by a period. For example $m^{2}-n^{2}/m^{2}+n^{2}$ is to mean $(m^{2}-n^{2})/(m^{2}+n^{2})$, and $a/bcd$ means ${\frac {a}{bcd}}$, but $a/bc.d$ means ${\frac {a}{bc}}d$.

This solidus notation for algebraic expressions occurring in the text has since been used in the Encyclopedia Brittanica, in Wiedemann's Annalen and quite generally in mathematical literature. The solidus may be viewed as a symbol of operation, denoting reciprocal in the same way as √ denotes square root and as — denotes reverse. The expression $/a$ is a sufficient notation for the reciprocal of $a$; in $1/a$ the figure 1 is redundant, just as in $0-a$ the 0 is redundant. The horizontal bar serves the two-fold purpose of a vinculum and a sign for reciprocal. When the reciprocal idea is detached and denoted by /, rules for the manipulation of / can be enunciated; thus $1/a=a$; $(/a)(/b)=1ab$, just as ${\sqrt {a}}{\sqrt {b}}={\sqrt {ab}}$. The notation of algebra is in fact planar; its complete reduction to a linear form is not a simple matter and was not tackled by Stokes, but this has been attempted by later writers, some of whom write $expx$ for $e^{x}$. One indeed has proposed to use \ for involution and | instead of a bracket so that $c|(d+e)^{3}$ would be written $c/|(d+e)\ 3|$.

In the winters of 1883-4-5 Prof. Stokes delivered in Aberdeen, Scotland, three courses of lectures on Light, under the auspices of the Burnett trust. In 1784 John Burnett, a merchant of Aberdeen, died, bequeathing a portion of his property to establish prizes for the best and next best essay on the following