Size for liability of carrying ink is enough to make two letters. Can be carried in form of dry ink, ink in feather, or ink in the inkwell. The gemara is unsure if these dif forms of ink can combine for the size.

Normally, you need to do a הנחה to the item to be liable- placing it down in the new location. If someone writes ink on paper as they are walking That is a form of הנחה bc the ink will permanently be on the paper so they are liable even if the paper doesn’t come to rest.

If one carries out half the size in one act and another half size in a second carrying, the two actions can combine for חיוב if the first item is intact still at the time the second item comes. If it was burned, taken by a dog, or if it’s size diminished by the time the second half size was brought, there is no חיוב.

Even though we require הנחה to be liable, if the object is carried through the domain less than 3 tefachim away from the ground, לבוד considers it as if its at rest on the ground. We don’t use לבוד for an item flying through a domain within 3 tefachim of the ground, though. In that scenario, there’s nothing linking the item to the domain at all.

Acc to r Yosi, for two actions of carrying to combine for the requisite size they must be carried to the same domain. If one carries half size to one street and another half size to a dif street they are exempt. The gemara has a dispute about what divides streets- either another private domain between them, even a karmelis, or even a large log.

Mishna said size the liability for eye paint is enough for one eye. This is for super modest women who covered one eye with a veil but for other women the size is for two eyes.

Size for wax is to put on opening of small hole of a wine barrel. Size for glue is enough to put on board that bird trappers use.

Lime is used to remove hair. Size for liability is enough to remove hair from finger of young girl. Poorer girls use lime, richer use flour, and daughters of Kings use שמן המור- special spiced oil or oil from olives that haven’t grown a third. R Yehuda says lime is liable in smaller amount of removing hair around the temples, and r nechemia says even the size of lime that is placed in the forehead to make the skin glow. Alternatively, lines of lime would be placed as measuring markers and that’s the size of liability.

Fine sand size for liability is enough to fertilize one Stalk of cabbage or leek. Coarse sand is the size to add to lime plaster. It sounds like our mishna holds sand is beneficial for lime plaster. However, we see that the rabanan actually say the opposite- sand ruins the brightness of plaster. This is evident in the law that after the Churban, one cannot use bright plaster unless they put in sand also. However, this law itself may be the reason why sand is significant to put in plaster in order to allow to be used.

A reeds size is enough to use as a pen that comes up to the joints of the fingers. If it’s unusable as a pen, then a reeds size is enough for fuel to cook an easily cooked egg. (Fig size from Egg of hen)