# General-formulae Sentence Examples

In the second of these notices he gives the

**general formulae**without demonstrations.What is more important is to verify particular examples of

**general formulae**.The

**general formulae**applicable to these cases are largely approximative.The

**general formulae**of § 54 (p being replaced (i) by 2m) may in the same way be applied to obtain formulae giving the area of the trapezette in terms of the mid-ordinates of the strips, the series being taken up to b 2f ul m or /th 2J ug m at least, where u is of degree 2f or 2f + I in x.The series will thus possess the following

**general formulae**M 2 CrO 4 M2Cr207 M2Cr30,0 &c. (M =one atom of a normal chromate bichromate trichromate monovalent metal.) Chromates.As corollaries to the

**general formulae**he adds the formulae relating to the representation of a number as a sum of five squares and also of seven squares.The fact that a question of which Smith had given the solution in 1867, as a corollary from

**general formulae**governing the whole class of investigations to which it belonged, should have been set by the Academie as the subject of their great prize shows how far in advance of his contemporaries his early researches had carried him.By continuing the introduction of methyl groups we obtain three series of homologous hydro carbons given by the

**general formulae**CnH2,i 4.2, CnH2n, and CnH2n 2, each member differing from the preceding one of the same series by CH 2.Miscellaneous Developments in Arithmetic. - The following are matters which really belong to arithmetic; they are usually placed under algebra, since the

**general formulae**involve the use of letters.