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With Master Turnill, the attachment to mathematics and algebra was a real love, though it was otherwise with Clare, who pursued these studies solely out of ambition, and with a hope of raising himself in the world. The desire to improve his position became stronger than ever after his return from Wisbeach.

While he had little leisure to himself, and much hard work, he was not averse to the society of friends and companions, either, as in the case of Turnill, for study, or, as with others, for recreation; but as soon as he found himself, to a certain extent, his own master, he forsook the company of his former acquaintances, and began to lead a sort of hermit's life.

How far mathematics and the pure sciences would help him on the road he did not trouble himself to consider; he only had a vague notion that they would lead him to be a 'scholar. So he toiled with great energy through the algebraic and mathematical handbooks purchased by friend Turnill, often getting so warm on the subject as to neglect his dinner-hour, in brown studies over the plus and minus, squares, cubes, and conic sections.

His friend and guide, John Turnill, subsequently promoted to a post in the excise was equally unable to throw light into the darkness of plus and minus, and after a few last convulsive struggles to get through the 'known quantities' into the unknown regions of x, y, and z, he gave it up as a hopeless effort.

In the latter favourite labour he was much assisted by a young friend, whose acquaintance he had made at Glinton school, named John Turnill, the son of a small farmer.