Keilim, Chapter 24, Mishnah 16. Our chapter consists of a lengthy chain of rulings, all shaped by a single formula: a common household object is sorted into three types, and each type is assigned its own place in the laws of tumah. In one form the object is used for sitting or reclining, and it is therefore susceptible to tum'at midras, the tumah transmitted by a zav (or someone in a comparable state of tumah) who sits or presses upon it. In a second form the object is never sat upon, yet it is a genuine utensil or article of clothing, so it can contract corpse tumah and the remaining kinds of tumah, though not midras. In a third form it does not qualify as a utensil at all and stays entirely tahor. Here the mishnah applies that three-way sorting to a woman's hairnet.
The object in question is the sevacha, a net of woven mesh that women placed over their hair. It filled more than one need: it warmed the head, it covered the hair for the sake of tzeniut, and it kept the hair gathered so that it would not fall loose.
The mishnah begins: "Shelosha sevachot hen," hairnets come in three varieties, and the halachah of each one differs.
"Shel yalda teme'ah tum'at midras." A girl's net is susceptible to tum'at midras. Hers was manufactured soft and cushioned, and at times when it was not being worn she would sit upon it. Because it doubles as a sitting place, it belongs among the objects that contract midras tumah.
"Shel zekenah teme'ah tum'at met." The net belonging to an elderly woman contracts corpse tumah, for it counts as a garment. Midras tumah, though, does not apply to it: a net of this sort was rigid rather than soft and padded, and no one would rest her weight on it. A garment, yes; a seat, no.
"Veshel yotzet lachutz tehorah miklum." The third net was worn when a woman left the house. It was a small covering laid over her ordinary hairnet, guarding both the net and her hair against rain and dirt. Of this one the mishnah rules "tehorah miklum," clean of every form of tumah. Since its role is nothing but protection, it is not reckoned a keli in its own right, and tumah cannot take hold of it. This parallels the protective gloves treated in the preceding mishnah: whatever exists solely to shield another thing from harm or grime is not itself counted as a vessel, and it therefore lies wholly beyond the reach of the tumah laws.
Three brief phrases thus cover the entire spectrum: the padded net of the girl, which doubles as a seat and takes midras; the firm net of the older woman, which is clothing and takes corpse tumah; and the outdoor rain cover, which is a mere shield and stays completely tahor.