Axial forces in a catenary

I’m using Hooke’s Law and the GH definition Daniel Piker posted on this thread for calculating the axial forces in a catenary cable that is only supporting its own weight. Do you think I’m obtaining the right values by adding the components shown in this picture?

And also, if I want to add a point load to the catenary, do you think the following axial force values truly correspond to the way tension forces would be distributed on a cable in real life?

Thanks for your attention! Here’s my GH definition: Axial forces in (25.8 KB)

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