knot theory – White’s equation in original paper

I’m reading this paper and I just want to understand a part of it.

In the section 2, page 698, I understand he’s working in his equation (known as the White’s equation)


but I don’t get why if $K'(t)=K(t)+epsilon v(t)$ with $0<epsilon$ small enough such that $K$ and $K’$ never overlap I can say that I’m calculating the Writhe of the curve $K$?

Sorry in advance if the question is simple, but I don’t understand well the notation and I have never used differential forms.