The linear invariant a s is such that, when equated to zero, it determines the lines ax as **harmonically** conjugate to the lines xx; or, in other words, it is the condition that may denote lines at right angles.

The whole disposition of pillars, posts, brackets and rafters is **harmonically** arranged according to some measure of the standard of length.

Turner has analysed **harmonically** the light-curves of a number of long-period variables, and has shown that when they are arranged in a natural series the sun takes its place in the series near, but not actually at, one end.