MEASUREMENT OF ANGLES. 29 



point where the index. marks the circle, say at 10, then turning 



-----R 



the index towards S, observe where it makes the circle, say 20, 

 the difference 10, is the angular distance of S from B. The 

 instruments of Ptolemy were constructed upon this principle 

 though not so perfect, using shadows, and other contrivances, 

 instead of simply observing through two vanes or sight holes. 



Ptolemy had not intended his system to be received other than 

 an hypothesis', which might account for the observed motions ; he 

 did not profess this to be the actual order of the world, but his 

 successors, without their great master's love for truth and careful 

 study, soon gave to these supposed spheres and orbs, a real exis- 

 tence, and the heavens became crowded with crystalline spheres 

 moring in all directions, and with all velocities, and as often as 

 new motions, or irregularities in the old ones were detected, new 

 circles moving at their centres round the old ones, were added, 

 called epicycles, so that at last cycles and epicycles, revolved in all 

 directions, bearing the planets along with them, until amid the 

 crowd of spheres and crystal orbs the brain grew dizzy, and could 

 not comprehend the mysterious revolutions. Amidst all this 

 confusion of " Cycle and epicycle, orb on orb," a bright 

 luminary arose, arid with a master iiand dashed aside the 

 crystal spheres of the successors of Ptolemy, substituting instead, 

 the simplicity of truth. This man was Nicholas Coperni- 

 cus. At the time when the true svstem was about'to be made 



