Re: The shape of the eye pupil

The reason some animals have what is called a "slit-form" pupil is 
because they were more successful over millions of years than 
animals with circular pupils that were competing for the same food and
habitat.  This leads to what I think your question meant to ask, 
which is: what advantage does a slit-form pupil give an animal?

Among mammals, the slit-form pupil is relatively rare.  It is found in
small cats and foxes (vertical), and in horses and goats (horizontal) --
probably more that I'm missing; I didn't do a thorough search.  In 
reptiles, I'm not familiar with it in lizards, but I do know that venomous
snakes have primarily vertical slit-form pupils, while non-venomous 
snakes generally have circular pupils.

A scientist named William Abbott performed some experiments in 1907
("Experiments On The Function Of Slit-Form Pupils", Toronto Univ.
Studies in Psychology v. 2) in which he measured the ability of humans
to distinguish discrete points with and without an artificial slit-form pupil.
He found that that ability was increased with a slit-form pupil perpendicular
to the plane in which the objects were located.

You will notice that all the animals listed above with vertical slit-form
pupils are predators, mainly on a single horizontal plane (the ground), 
and mainly of small animals.  In this case, the shape of their pupil allows
them to focus more sharply on their prey.  Lions and wolves, by 
contrast, hunt large prey and might not gain any particular advantage
from a slit pupil, even though they are in the same families, respectively,
as cats and foxes.

This doesn't reasonably explain to me what horses and goats (and any
other animal) could gain from having a horizontal pupil.  In the case of
mountain goats, perhaps it helps them navigate the vertical surfaces of
a mountain -- and maybe the modern goats have retained the pupil in
that form even though it's no longer useful for that purpose.

I hope this at least partially answers your question!