Of these three ways of writing the expression, the last is evidently to be preferred : the other two are ob jectionable, not from any deficiency in clearness, but from a certain want of symmetry, which is very per ceptible in both of them.
NIodein analysts have frequently had occasion to se parate the symbols of operation from the quantities on which they act, an artifice which gives great concise ness to a variety of theorems : this separation has been marked in different ways, either by a dot, or the sign of inultiplication, or by parentheses : in some instances the double dot (:) has been employed. As it is very desira ble to confine each symbol to one meaning, the last plan, or the two dots, is the least objectionable for this pur pose, and can create no ambiguity, since it has become entirely obsolete in the best writers in any other sense. The theorems of Lagrange would be thus written.
The met its of the two systcms of notation employed in the differential calculus have been discussed by Euler, in the preface to his Institutiones Calculi Integralis, and more fully, by Mr. Woodhouse, in the preface to the Analytical Calculations. The supetiority of the use of the (1 over the system of dots has become so very appa rent, that the course of a few years will, in all proba bility, render the latter obsolete, a circumstance which induces us to forbear entering into any lengthened detail of their comparative values, and to content ourselves with merely indicating a few of the grounds for reject ing the latter: these are, 1st, The uncertainty which may arise respecting the letters to which the indices refer, and the confusion which arises from having two indices to a letter. 2(1. The want of analogy with other
established notations, such as those relating to the sym bols and 3(1, The great difficulty, il not the im possibility, of representing, by their means, theorems relating to the separation of operations front quantities.* NOrl'AWAY, a county of Virginia,lhounded east by Dinwiddie, south hy Brunswick, and Lunenburg ot Not taway river ; north-west by Prince Edward; and north east by Amelia. Length, 22 ; mean width, 12 ; and area 264 square miles. It is watered by some branches of the Appomattox, and by the Nottaway and its branches. Staples, cotton and tobacco. The chief town, Hender sonville, is 45 miles south-west by west from Peters burg.