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-- All meridians of longitude have the same length ... they all join the north and south poles. -- Each parallel of north latitude has the same length as the parallel at the equal south latitude, but no other one.
Every line of constant longitude joins the north and south poles. Therefore the length of every line of constant longitude is one half of the earth's polar circumference.
You may be thinking of the distance between lines of longitude. The length of the lines of latitude decrease because the Earth is round, so the length of the line is shorter at the poles than it is at the Equator. The distance between the lines of longitude is shorter as you move toward the poles, again, because the Earth is round. All lines of longitude are the same length.
1 degree longitude or latitude? What day of the year? Middle of winter, 1 degree latitude, no daylight. But middle of summer same place, 24 hours.
Technically and mathematically, the length is the onlything that affects its period.