He found that before he could make a good achromatic telescope it was necessary that he should calculate his curves from data depending upon the nature of the glass.

He accordingly proceeded to study the optical laws of refraction, in which his knowledge of geometry and mathematics greatly helped him.

And in course of time, by his rare and exquisite manipulative skill, he succeeded in constructing a four-inch refractor, or achromatic telescope, of admirable defining power.
The excellence of his first works became noised abroad.

Astronomical observers took an interest in him; and friends began to gather round him, amongst others the late Professor Phillips and the Rev.Vernon Harcourt, Dean of York.

Cooke received an order for a telescope like his own; then he received other orders.