W Synonyms

W Sentence Examples

• The principle is readily adapted to the determination of the relative densities of two liquids, for it is obvious that if W be the weight of a solid body in air, W, and W2 its weights when immersed in the liquids, then W - W, and W - W 2 are the weights of equal volumes of the liquids, and therefore the relative density is the quotient (W - W,)/(W - W2).

• The heating at the surfaces, the variations in their smoothness, and the variations of the lubrication make continuously variable, and necessitate frequent adjustment of W or of the nuts.

• In order to obtain the seminvari ants we would write down the (w; 0, n) terms each associated with a literal coefficient; if we now operate with 52 we obtain a linear function of (w - I; 8, n) products, for the vanishing of which the literal coefficients must satisfy (w-I; 0, n) linear equations; hence (w; 8, n)-(w-I; 0, n) of these coefficients may be assumed arbitrarily, and the number of linearly independent solutions of 52=o, of the given degree and weight, is precisely (w; 8, n) - (w - I; 0, n).

• It is shown in the article on Combinatorial Analysis that (w; 0,n) is the coefficient of a e z w in the ascending expansion of the fraction 1-a.

• We may, by a well-known theorem, write the result as a coefficient of z w in the expansion of 1 - z n+1.