The power of a combination of two cog-wheels is ascertained by multiplying the distance at which the power is applied from the centre of the first wheel, by the radius of the second wheel ; and dividing that sum by the sum of the distance at which the resistance acts from the centre of the second wheel, multiplied by the radius of the first : the quotient will represent the ratio of the power to the resistance it is able to overcome. In a combination of any number of teethed wheels the power of the system may be ascertained by taking the radii of the wheels as the even terms of a series, and the distances at which the power and resistance act from the centres of their respective wheels as the odd terms (or the intermediate ones) of the series ; then the pro duct of the odd terms, divided by the product of the even terns, will represent the ratio of the power to the resistance. The even terms will in this case represent the flyers or drivers, and the odd ones the followers, and the product of the former will give the velocity of the power, whilst that of the latter will give the velocity of the weight or resistance.
Very good practical rules, and examples for their application, of the relations of the various parts of a system of wheel-work are to be found in the Memorandum-book of Mr. Telford, inserted in his ' Biography,' and reprinted in the Engineer's Pocket Book ; ' but none of these easy practical solutions of the mechanical problems involved in this branch of applied mechanics, can dispense the engineer from the study of their principles. These are discussed at considerable length in such works as those previously mentioned, and in 3loseley's 'Mechanics applied to the Arts ; ' his work on ' Engineering and Architecture ; ' in Warr's ' Dynamics ; ' Weisbach's Mechanics of Machinery ; ' Borgnis, Trait4 complet de 3I4canique appliqu4e aux Arts ; ' Dupin's G4oinetrie et M4canique den Arts ;' Lanz et Bdtan court, Essai sur la Composition des Machines,' &c.; and to them the student is earnestly referred.