Rambam - 1 Chapter a Day

That impurity never returns. Ritual impurity applies only to keilim, functional articles. When these articles are broken, they are no longer considered keilim and, hence, no longer impure. See also Chapter 18, Halachah 10.

As stated in the following halachah, this is a Rabbinic decree. According to Scriptural Law, once they are broken, they are ritually pure.

If they are immersed while broken, they still return to impurity when new keilim are formed after they have been melted down.

I.e., for an article to regain purity, it must be immersed in a mikveh. Even so, it does not become pure on the day of its immersion, only after the appearance of three stars that night (see Hilchot She’ar Avot HaTum’ah 10:1).

As explained in Hilchot Parah Adumah 11:1, after a person or an article contracts impurity from a human corpse, the ashes of the red heifer must be sprinkled on him or it on the third and seventh day afterwards. After the sprinkling of the ashes on the person or article, he or it must be immersed in a mikveh. Unless the ashes are sprinkled on both those days, the person or the article does not regain purity.

There is a difference between the Rambam and the Ra’avad concerning this halachah. Some commentaries maintain that the Ra’avad objects to the Rambam’s wording here which could be interpreted — as could the wording of his Commentary to the Mishnah (Keilim 14:6) — as meaning that it is sufficient to sprinkle the ashes of the red heifer on the unformed mass of metal after it was melted down, even though it was not formed into a new k’li. The Ra’avad objects and maintains that metal can be purified only when a k’li is whole, either before it was melted down and reformed or afterwards. The Kessef Mishneh maintains that support can be found for both perspectives.
Tosafot Yom Tov [to the above-cited mishnah], however, interprets the difference of opinion in another manner. Both the Rambam and the Ra’avad require the k’li to be whole while the purification activities are performed. For when it is melted down, it is not impure and does not have to be purified. The Rambam, he maintains, requires all. the activities for the purification to be performed either before the melting or for all to be performed afterwards. The Ra’avad maintains that the first sprinkling can be performed before the melting and the second afterwards.

I.e., iron from a k'li that had contracted impurity and been melted down without being purified.

Which would produce ordinary earthenware utensils that are susceptible to impurity.

Utensils made from them are not susceptible to impurity (Chapter 1, Halachah 6).

The Zair Zahav to the Tosefta, Keilim 8:2, which interprets this as referring to a base metal k’li that is coated with gold.

The Kessef Mishneh and other commentaries have noted that the standard version of the Tosefta reads directly opposite from the Rambam’s text, stating that a pure k’li coated with impure material is pure, but a k’li made from impure coating is impure. Moreover, that version is more appropriate, based on the principles explained by the Rambam previously, because the coating of keilim is not susceptible to impurity (see Chapter 4, Halachah 4). And, as implied above, when a new k’li is made from impure metal, it is impure. Nevertheless, the authoritative manuscripts and early printings of the Mishneh Torah follow the text cited here.

Chapter 11, Halachah 21, spoke of a two-edged hatchet. The thick side would be used for chopping logs and the thin side for the delicate work of a carpenter. Here apparently the intent is a one-edged hatchet.

It was common to coat a heavy iron hatchet with steel so that the blade would be sharper and cut better [see the Rambam’s Commentary to the Mishnah (Keilim 13:5)].

For, as explained in Chapter 4, Halachah 4, a coating is not susceptible to impurity.

Containing beverages.

As mentioned in Halachah 2, the impurity of such a k’li is of Rabbinic origin.

There is a general principle that one Rabbinic stringency is not used to compound another (Shabbat 11b; see the following halachah). Thus since both the impurity of a false divinity and that of a reformed metal k’li are of Rabbinic origin, there are grounds to say that, in this instance, the reformed k’li should be pure. Moreover, there are commentaries (and some support for their view can be taken from Avodah Zarah 52a, the source for this law) who maintain that because of the severity of the prohibition against the worship of false deities, an exception should be made, but not with regard to other Rabbinic sources of impurity. The Rambam, however, clearly states that all types of Rabbinic impurity are considered the same in this context.

Chapter 1, Halachah 5.

In which instance, broken pieces can be subject to impurity (Chapter 18, Halachot 10, 13-14).

In his Commentary to the Mishnah (Keilim 30:1), the Rambam explains that it is common to make a wider base, like a bowl, for glass utensils as support. The Rambam — and the mishnah, his source — are speaking about an instance where the utensil itself was broken, but this bowl remained intact.

For then they no longer appear as broken keilim and are comparable to new keilim (ibid.).

Which would not be possible because its mouth is broken.

And it is possible to pour from it even when its mouth is broken.

Hence when the mouth is broken, it is no longer useful at all.

And susceptible to impurity.

Foods are left in them to pickle in wine or vinegar. Since a person is not inserting his hands into them frequently, the fact that the mouth is broken is not significant (ibid.:4).

I.e., it is considered as no longer useful as a k’li and hence, no longer susceptible to impurity.

Significantly, in his Commentary to the Mishnah (ibid.:3), the Rambam reverses these points, speaking of the majority of the circumference and a third of the height.

The Ra’avad offers a different interpretation of the above mishnah. The Kessef Mishneh justifies the Rambam’s interpretation.

For these are not effective seals for glass. See a parallel in Chapter 20, Halachah 3.

Even if the hole is merely in the upper portion, it is no longer considered functional.

Because the majority of the k’li is functional.

Because it is not functional.

Hot liquids are more likely to cause a crack to expand and then to seep through it than are cold liquids.

Because the utensil can be used despite the crack.

Even though the utensils can be used for cold liquids, since they cannot be used for hot liquids, they are not considered functional.

But they are still functional entities.

See Chapter 9, Halachah 16, which speaks of a metal dispenser. In his Commentary to the Mishnah (Keilim 30:4), the Rambam explains that a glass dispenser has a similar form. It is not considered as a utensil, because it has no base and is not a container. As stated in Chapter 1, Halachah 5, our Sages did not issue a decree with regard to a flat glass k’li.

A divider that enables one to see the objects on its other side [Commentary to the Mishnah (Keilim 30:4)].

This is not significant, for that is not the way it is intended to be used.

Because a change was not made in its physical substance to alter its form. A change in intent cannot alter the status of a utensil, only a change in its form. See Chapter 8, Halachah 10.

For its primary function is not that of a container.

See Chapter 5, Halachah l; Chapter 8, Halachah 1.