The following is a simple method of establishing the formula for the determination of the duration of day, at any latitude, for a known declination of the sun.

terminator or limit of the sun's illumination of the earth (at right angles to the line showing the direction of the sun's rays), ά is the point at which the terminator, άO'c', cuts the elevation of the line of latitude λ.

Referring to the plan, α and α are the points in plan corresponding to ά in elevation ; 0 is the plan of the polar axis.