MISHNA I.: In the following cases the decisions of Beth Shamai are lenient, and those of Beth Hillel rigorous. An egg laid on a holiday is, according to Beth Shamai, allowed to eat on that day, but is not so according to Beth Hillel. Regarding the removal of leaven (before Passover) Beth Shamai hold it must be of the size of an olive and leavened bread of that of a date, while the Beth Hillel fix the size of each at that of an olive.
MISHNA II.: All agree in that a cattle born on a holiday is allowed, but a fowl out of the eggs is not. If one slaughter game or fowl on a holiday he is allowed by Beth Shamai to dig up loose ground (the spade already struck in) and cover the blood, while Beth Hillel do not allow to kill unless there be earth prepared, admitting, however, that after one has killed, he may use with the spade the loose ground, and that ashes from the hearth be regarded as prepared earth.
MISHNA III.: The Beth Shamai consider ownerless everything left to the poor, while according to Beth Hillel, only that is ownerless which is abandoned to the rich as well, instance Shmitah. If all the sheaves of a field contain each a Kab and one of them containing four Kab is left, the Beth Shamai do not regard it forgotten, and Beth Hillel do so. (Tract Peah, Chapter VI.)
MISHNA IV.: Likewise do not Beth Shamai regard forgotten a sheaf left near a wall, a stag, a bull, or implements; while Beth Hillel do.
MISHNA V.: The four-year-old vine is, according to Beth Shamai, not subject to either the additional fifth or destruction, while according to Beth Hillel it is. Furthermore, the former hold that it is subject to both Peret and oilleloth [Lev. xix. 10], and that the poor are to redeem it themselves; while the latter say it all goes to the winepress.
MISHNA VI.: A cask with preserved olives need not have a hole, so Beth Shamai, while. Beth Hillel find it obligatory, admitting, however, that if there had been one, but was stopped by the dregs, the cask is clean. If one, having besmeared his body with sweet oil, became unclean and then took a legal bath, Beth Shamai declare him clean even when the oil is dripping, but according to Beth Hillel he is not clean, unless there be left on him no more oil than would be necessary to besmear a small organ, which last condition the Beth Shamai require when the oil used before the bath was unclean, while Beth Hillel in this case require that there be only an inconsiderable moisture. Said R Jehudah in the name of Beth Hillel: That there be a moisture sufficient to moist some other thing. (All this will be explained in Tract Taharath.)
MISHNA VII.: According to Beth Shamai one dinar or its worth is consideration in the marrying of a wife; the Beth Hillel set it down at a Perutah or its worth, which is one-eighth of the Italic Saar. The former hold further that one may dismiss his wife on the basis of the old divorce bill, i.e., a divorce after whose consummation he remained yet alone with his wife, while the Beth Hillel say he cannot. Similarly, if a wife who had been divorced, happened to pass a night in the same inn with her (former) husband, she needs no other bill of divorce according to Beth Shamai, but the Beth Hillel say she needs one if she was divorced after they had been wedded, but not after they had been only betrothed to each other, for in the latter case they were not yet intimate with each other.
MISHNA VIII.: Beth Shamai allow brothers to enter levirate marriage with their rival-wives (of prohibited kinship degrees), which the Beth Hillel forbid. If they have performed Chalitzah, Beth Shamai declares them unmarriageable to a priest and Beth Hillel allows them. The two schools change their views regarding the case when the wives become widows after they had been taken in levirate marriage. Notwithstanding that the one school prohibits what the other allows, the disciples of the two schools have never refrained from intermarriage with one another. Likewise as regards cleanness and uncleanness where the two hold opposite opinions, they have none the less never hesitated to loan one another objects declared clean by both schools.
MISHNA IX.: If of three brothers two are married to two sisters and the third one is single; if, now, one of the married brothers died and the unmarried promises the widow to marry her, whereupon the second of the brothers died, Beth Shamai say: The single brother is to keep his wife and the other one is to go free as the wife's sister; while Beth Hillel hold that he must dismiss his wife with both divorce and Chalitzah, and his sister-in-law with Chalitzah; as the proverb goes: He is to be pitied for both his wife and his sister-in-law! (Tract Yebamoth, Chapter IV.)
MISHNA X.: If one abstain by vow from sexual intercourse with his wife, he is allowed by Beth Shamai to keep the vow for two weeks, by Beth Hillel for but one. A woman who bears a miscarriage on the eve of eighty-on-e days (after the birth of a daughter) Beth Shamai free from an offering, and Beth Hillel hold liable. Beth Shamai say a quadrangular sheet needs no tzitzis, Beth Hillel hold it needs. A basket with figs prepared for Sabbath is, according to Beth Shamai free from the tithe, according to Beth Hillel it is not.
MISHNA XI.: If one vowed to remain a Nazarite for some time, and after the expiration of the term comes to the land (of Israel), Beth Shamai hold he must continue in the state of Nazarite for another thirty days, while Beth Hillel make him begin the whole term anew. If two parties of witnesses testify, the one that so and so has vowed to be a Nazarite twice, the other, five times, Beth Shamai declare this testimony invalid as conflicting, and he must not be a Nazarite at all, while Beth Hillel say: Five contains two, hence he must be a Nazarite twice. (Nazir, Chapter III.)
MISHNA XII.: The man who finds himself underneath a crevisse does not, according to Beth Shamai, transfer the uncleanness from one side to the other, while Beth Hillel regard the man as hollow, so that his upper side does transfer the uncleanness (as roofing). (Oheloth, Chapter XI.)
Sources: Sacred Texts