A "family heirloom" (air-loom) is an item that has been passed down to different family members through the years. saying that the item has been "passed down for generations" provides the same meaning as saying "family heirloom"
"family heirloom"（家宝）（air-loom）は、年月をかけて家族に受け継がれている物です。物が"passed down for generations" （世代に受け継がれた）は、"family heirloom"（家宝）と同じ意味です
1. Ancestral = of, belonging to, or inherited from an ancestor or ancestors.
"I live in the family's ancestral home."
2. hereditary = relating to inheritance; relating to money or possessions that are passed down to one's relatives.
1. Ancestral = 先祖代々の、先祖から受け継がれた、
"I live in the family's ancestral home."
家族の先祖代々の家に住んでいます。
2. hereditary = 先祖から受け継がれたお金、所有物など
This kimono has been passed down from generation to generation.
「成人式の着物はたいてい母から子へ代々受け継がれます」="The kimonos worn at coming-of-age ceremonies are usually passed down across generations from mother to child."
「代々受け継がれます」というのは英語で"passed down across generations/from generation to generation"と言います。後者はちょっと長めですが、意味はほとんど同じです。
「ちなみに私は叔母の着物を着ました」＝"By the way, I wore my aunt's kimono."と言います。
The kimono has been passed down from generation to generation
The term heirloom means when an item has been in your family for many years and has been owned by different people and stayed in the family.
The term generation to generation means that it has been used by great grandmother/father to grandmother/father to daughter/.son and stayed in the same family.
heirloomは、先祖代々受け継がれてきたものを表します。
generation to generationは、曾祖父母から祖父母、そして娘息子へと、代々使われてきたことを表します。
This has been handed down generation to generation.
This has been passed down from generation to generation.
The phrases passed down and handed down adequately describe this situation.
For example: This kimono has been handed down from generation to generation.
This kimono has been passed down from generation to generation.
passed downとhanded downで、この状況を適切に表現できます。
例文
This kimono has been handed down from generation to generation.
（この着物は代々受け継がれてきました）
This kimono has been passed down from generation to generation.
（この着物は代々受け継がれてきました）
This kimono has been passed down generation to generations
This kimono belonged to my great grand-mother and it's been passed down the family since
When you want to explain that a kimono you are wearing has been passed down generation to generation:
-This kimono has been passed down generation to generations
-This kimono belonged to my great grand-mother and it's been passed down the family since
あなたが着ている着物は代々受け継がれてきたと言いたい時、以下のように言えます：
This kimono has been passed down generation to generations.
（この着物は代々受け継がれてきました。）
This kimono belonged to my great grand-mother and it's been passed down the family since．
（この着物は祖祖母の物で、以来代々受け継がれてきました。）
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イギリス 
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