the definition of second, except in certain phrases like "every other day").

The Latinate series 'primary', 'secondary', ... is often used for importance, or precedence ('primary consideration') and sequence of dependence ('secondary effect', 'secondary boycott', 'secondary industry'), though there are other uses as well ('primary school', 'primary election'). The first two in the sequence are by far the most common; 'tertiary' appears occasionally, and higher numbers are rare except in specialized contexts ('quaternary period').