Why HE not remain constant with change of latitude

Why HE not remain constant with change of latitude

Heeling error changes with:
Change in course.
Change in latitude.
Change in angle of heel.

Change in course:
HE changes with change in course. Why?
We know, deviating force acts athwartship. Since HE error cause: Ship’s permanent component (R).
Induced by Z into VSI, acting through the compass position.
Induced by Z into athwartship HSI, when vessel heels.
As a result,
Max HE deviation on N or S heading.
Zero HE deviation on E or W heading.

Change in latitude:
We know,
If magnetic latitude increase, Z get bigger, DF(H) get smaller.
If magnetic latitude decrease, Z get smaller, DF(H) get bigger.
Since HE error cause: Ship’s permanent component (R).
Induced by Z into VSI, acting through the compass position.
Induced by Z into athwartship HSI, when vessel heels.
Therefore, HE change with change in latitude.

Change in angle of heel:
Since HE error cause: Ship’s permanent component (R).
Induced by Z into VSI, acting through the compass position.
Induced by Z into athwartship HSI, when vessel heels.
As a result,
If Angle of heel increase, HE increase.