PIC24H delta time calculation
I don't see where you're declaring delta_t anywhere. This is also true for final and initial (delta_t= final - initial;). I would imagine that final is really final_time, and initial is really init_time, but why are you asking a question about code that isn't from your actual project?

Please post code that actually compiles.



On delta_t = (unsigned long)((delta_t/(CLOCKS_PER_SEC*1.0))*1000;

Why are you converting to a float, and then back? You don't need to. 
Instead, divide CLOCKS_PER_SEC down so it's CLOCKS_PER_MILLISEC. Then you can do everything with ints:
delta_ms = (delta_clocks/(CLOCKS_PER_SEC/1000));

This needs no type-conversion, and will be MUCH faster.

Note: I've renamed some of your variables for better understandability.