I think I am not understanding correctly the difference between 'mavlia' and 'mekader'. I understand that mavlia means that the two people stand on opposite sides of the valley, and extend the 50 amos rope over it. Whereas with mekader, they have to measure with a 4 amos rope, and do down the slope and back up again. However, doesn't the measurement actually end up being the same, because even with 'mekader' the line is measured in a straight line, with the guy higher up holding the rope by his feet. In essence, only the horizontal measurement is taken into account, and the slope is ignored. So what is the difference?
For example, the gemora says that a valley deeper than 2000 amos, even if its less than 50 across, should be measured by mekader, not mavlia. But what is the difference in the measurement at the end of the day?
Thanks
Reuven
Technically speaking you're right. If the measurement is precise with the 4 amos rope it will end up being the same, and maybe even more lenient, because a long rope has more lag over distance. However in the case you mentioned, when it is a deep valley and they do kidur, the eiruv will end somewhere in the valley and not further away, so kidur has some elements of chumrah as well, this according to Rashi. (According to the Rosh one measures the valley's descent normally until the end of 2000 amos. It is unclear to me how mekadrim would work on such a steep slope.)
The only real difference in short ropes is that they enable a more precise measurement of the ravine, since Chazal felt that long ropes could not be used as they have some lag over distances.
Yoel Domb
I believe that the artscroll explains that mekader is not necessarily horizontal. it depends on the angle of the slope.