Understanding “um so schneller” in this Kafka sentence

Question

What is the contribution of um and the comparative form of schnell to the meaning of this sentence in Kafka’s Der Verschollene?

Und da das Ärgste ausgesprochen war, drängte alles andere um so schneller nach, er sagte, ohne die geringste Lüge zu gebrauchen, Dinge, an die er gar nicht eigentlich vorher gedacht hatte.

Another way to put this question may be to ask how the sentence above is different from:

Und da das Ärgste ausgesprochen war, drängte alles andere so schnell nach, er sagte, ohne die geringste Lüge zu gebrauchen, Dinge, an die er gar nicht eigentlich vorher gedacht hatte.

I can only come up with the following guess (by a blind, mechanical application of grammar and meaning): alles andere came out faster (schneller) than das Ärgste, and the degree (so) by which that Nachdrängen was faster is not exactly but only approximately (um) as set out in the er sagte clause.

But this kind of precision seems out of place for the situation (we’re not measuring the speed of some projectile). Maybe um + a comparative form of adverb has a special usage I am not aware of.

Answer 1

um so is the old spelling of umso.

The meaning of umso is:

Konjunktion, die einen Komparativ verstärkt

Conjunction that reinforces a comparative form of an adjective

Thus, in your example it means: Because the worst [I assume: point of criticism] is already spoken aloud, it is even more easy to say other (smaller) [points of criticism], too. They burst out even faster and he says, without lying, even things he hadn't thought about before.

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Um so in Verbindung mit je zeigt an, dass sich etwas proportional zu etwas anderem verändert, z.B. Je schneller der Wagen, umso größer die Gefahr

The combination of um so + je shows the proportial change of two things, synomym to desto, e.g. The faster the car, the higher the danger

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