From the data thus obtained an **isobaric** map and a report are prepared for each day; and weather warnings are telegraphed to any part of the coast when necessary.

Two of these show that the leading coefficient of any covariant is an **isobaric** and homogeneous function of the coefficients of the form; the remaining two may be regarded as operators which cause the vanishing of the covariant.

The number of different symbols a, b, c,...denotes the the covariants are homogeneous, but not in general **isobaric** functions, of the coefficients of the original form or forms. Of the above general form of covariant there are important transformations due to the symbolic identities: - (ï¿½b) 2 2)2 = a b - a b; (xï¿½ = as a consequence any even power of a determinant factor may be expressed in terms of the other symbolic factors, and any uneven power may be expressed as the product of its first power and a function of the other symbolic factors.