William Henry Thompson, a mathematician, proved in a paper published in 1880 that it was impossible to achieve the 5040 changes using the normal bobs only, without the use of singles or some other type of call. This result had long been suspected by peal composers, but it had not been proved. Peal length round blocks of caters and cinques were more easily achieved. However, the ringing of Grandsire at these stages was limited by the relative rarity of towers with sufficient bells, and Grandsire Caters was first rung to a peal length in 1717 and Grandsire Cinques in 1725.