Thus we shall be able to specify the system completely when the number of variables, viz.
This is of degree 8 in the coefficients, and degree 6 in the variables, and, for the canonical form, has the expression -9m 6 (x 3 +y 3 +z 3) 2 - (2m +5m 4 +20m 7) (x3 +y3+z3)xyz - (15m 2 +78m 5 -12m 8) Passing on to the ternary quartic we find that the number of ground forms is apparently very great.
Roberts's list of southern variables (ibid.
We thus recognize two classes of variables, of which (I) the long-period variables have periods ranging in general from 150 to 450 days, though a few are outside these limits, and (2) the short-period variables have periods less than 50 days (in the majority of cases less than io days).
To these must be added the external variables of temperature and pressure, and then as the total number of variables, we have r (n+I) + 2.