The slopes of the parabolas

Let us calculate the slope of the parabolas:

$${d\tau \over dm}= {X^2 \over 2 \sqrt{X^2 m+ T^2}}.$$ (8)

The slope at m=0 is

$${d\tau \over dm}= {X^2 \over 2 T}.$$ (9)

The distance between two adjacent hyperbolas when the sloth space is evenly sampled is

$$\Delta t = {x^2 \over t} \Delta m.$$ (10)

Hence the slope of parabolas at m=0 is proportional to the distance between hyperbolas passing through the corresponding points. From Figure  we can see that at higher times the slopes are nearly the same (the lines appear to be parallel); this conclusion corresponds to the fact that hyperbolas divide the gather quite evenly.