Jockey's cap, clam shells and velvet rhombuses stitch together the tales of 19th century women convicts sent to Australia, modern-day male prisoners, the persecuted and the privileged alongside a couple of Britain's most famous artists in a new show.

Quilts: 1700-2010 at London's Victoria and Albert museum reveals the shape of history in a quilting display that tells the stories of struggle, loss and longing over a timeline that stretches back to before America threw off its colonial masters and when crooks were packed off to the far side of the world.

Turner Prize-winning artists Grayson Perry and Tracey Emin have both provided thought-provoking contributions, but one of the gripping highlights of the show is the floor-to-ceiling Rajah Quilt on loan from Australia.

The quilt is named after the ship on which 180 British women convicts sailed to Tasmania in Australia in 1841 after they were sentenced to "transportation".

The women used sewing provisions and textiles donated by Elizabeth Fry's social reform initiative to create what is now the only transportation quilt in a national collection, never before shown outside Australia.

When the Rajah arrived in Hobart on July 19, 1841, the textile supplies had been turned into an inscribed patchwork, embroidered and appliqué coverlet, which was presented to the governor's wife as evidence of the women's industry.

Made using the pieced-medallion style common in the late 18th century, its central panel is worked with broderie perse, a term used to describe appliquéd chintz, probably because of its supposed resemblance to Persian embroidery.

The V & A show is popular and has attracted interest across Britain and from across the Atlantic in America, where quilting remains a popular activity.

Assistant curator Claire Smith said quilting was a way of documenting your own history and said research for the exhibition had revealed touching and intimate family histories.

Ms Smith said a small cot quilt probably from the 1690s was known only to have been made by the Governor of Deal Castle's daughter Priscilla Redding.

"Research for the exhibition uncovered Priscilla's diary chronicling the religious persecution of her father for being a Baptist preacher, the near drowning of her daughter and the death of her oldest son at the age of 15; very important and poignant family events," Ms Smith said.

Grayson Perry's 1993 Right to Life is a comparatively small but dramatic and disturbing quilt of red, white and black velvet. Its intricate designs of rotating foetuses contradicts the regularly perceived role of a quilt as an object of warmth and comfort and creates an unsettling commentary on the American abortion debate of the 1990s.

Designed by Perry it demonstrates the use of modern technology in craft and was professionally stitched by computer-controlled embroidery.

Ms Smith said the bedroom has always been a site for incredible decorative display and Tracey Emin's quilt To Meet My Past - arranged on a bed - provides a confessional installation which follows the tradition of quilts used as vessels for personal and collective memories.

Caren Garfen's How Many Times Do I Have To Repeat Myself 2010 centred around women, the workplace and home. Fluff from domestic clothes dryers was collected by women in an aligned study and trapped within the quilt as an analogy of women trapped into working due to financial pressures when in reality they would prefer to remain at home.

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