So if Africa were refrigerated first, there would be considerable difficulty in the tropical productions of Africa escaping into the still hot regions of India.

Here again you would have to bridge over the Indian Ocean within so very recent a period, and not in the line of the Laccadive Archipelago.

If you suppose the cold to travel from the southern pole northwards, it will not help us, unless we suppose that the countries immediately north of the northern tropic were at the same time warmer, so as to allow free passage from India to Africa, which seems to me too complex and unsupported an hypothesis to admit.
Therefore I cannot see that the supposition of different longitudinal belts of the world being cooled at different periods helps us much.
The supposition of the whole world being cooled contemporaneously (but perhaps not quite equally, South America being less cooled than the Old World) seems to me the simplest hypothesis, and does not add to the great difficulty of all the tropical productions not having been exterminated.

I still think that a few species of each still existing tropical genus must have survived in the hottest or most favourable spots, either dry or damp.

The tropical productions, though much distressed by the fall of temperature, would still be under the same conditions of the length of the day, etc., and would be still exposed to nearly the same enemies, as insects and other animals; whereas the invading temperate productions, though finding a favouring temperature, would have some of their conditions of life new, and would be exposed to many new enemies.