The maximal altitude of the
Sun on a given day depends on the latitude of the observer and the
time of the year. The celestial equator intersects the meridian at
an altitude equal to the colatitude. This is equal to the maximal
altitude of the Sun at the equinoxes. To get the the maximal
altitude of the Sun
we must add the declination if we are in the northern hemisphere
or subtract the declination if we are in the southern hemisphere.
But if the answer comes out bigger than 90, we must instead subtract
the answer from 180.
In order to do this in a uniform way, we can instead use the following convention. We will measure altitude along the meridian from the south point on the horizon. So an altitude of 80 would mean 80 degrees in the south, while an altitude of 100 would mean 80 degrees in the north. In that case, the formula becomes 90 - latitude + declination.