362 Mr. BappaGE on the Influence of Signs 
on principles, which cannot be neglected without danger, or vio- 
lated with impunity ;—the authority of the greatest geometer of 
the age, failed to make converts to the language he had invented, 
whilst the justice of the view he had taken, was admitted, and 
his explanations almost universally adopted. Whilst the language, 
in which the Theory and the Calculus of functions are conveyed, 
is pointed out as a warning, not to be neglected by the most 
successful, that of the Mechanique Analytique of the same author, 
may perhaps be held up to imitation, with fewer limitations than 
any other work of equal magnitude. In returning to the notation 
of Leibnitz, Lagrange has ‘in this work, reduced the whole theory 
of mechanics to the dominion of pure ‘analysis, and in the choice 
of his symbols has frequently displayed that happy selection, 
which so much facilitates the process of reading and comprehend- 
ing analytical formule. 
The value of symmetrical symbols is greater in proportion to 
the complexity of the operations, and the number of quantities, 
which are concerned; but unless their selection is attended to at 
the outset of our studies, it is not to be expected that a correct 
taste can be acquired, I would therefore recommend a degree of 
attention to this subject, which is not usually bestowed on it by 
elementary writers: Some instances I shall select from the simplest 
applications of Algebra to Geometry. The equation of a right 
line is usually written thus: 
y=ar+h, 
which is sufficiently convenient. M. Biot in his Geometrie Ana- 
lytique * has employed this notation, as also has M. Hachette in 
his Introduction to the admirable work of Monget: both authors 
in treating of lines referred to three co-ordinates have denoted it 
thus: 
yYy=art+a, 
© P30: + Application de l’Analyse a la Geometrie, 4™* ed. p. 2. 
