30 



MECHANICS. 



seldom "as possible, in order to avoid 

 inequality of wear. For example, let us 

 suppose that the number of teeth in a 

 wheel were exactly ten times the num- 

 ber of leaves in the pinion ; each leaf in 

 the pinion would engage every tenth 

 tooth of the wheel, and would work in- 

 evitably on the same ten teeth every 

 revolution of the wheel. If it were 

 possible that all the teeth and leaves 

 could be constructed with mathematical 

 precision, and perfect and absolute si- 

 militude, and that no accidental differ- 

 ence, owing to any want of uniformity 

 in the material of which they are 

 formed, could exist, this would be a 

 matter of no consequence, and the 

 wear would still be even and equable. 

 But as these perfections never can exist, 

 the inevitable inequalities incident, as 

 well to the nature of the material of which 

 wheels are constructed as to the forms 

 they derive even from the most perfect 

 mechanical construction, must be com- 

 pensated by making the teeth and leaves 

 work, so that each leaf shall succes- 

 sively engage with all the other teeth of 

 the wheel before it engages a second 

 time with any one of them. 



This is accomplished by making the 

 number, of teeth and the number of 

 leaves prime to each'other, that is, such 

 that no integer divides both exactly. 

 The manner in which this is commonly 

 4one, is by making the number of teeth 

 such, that it is just one more than a 

 number which is exactly divisible by the 

 number of leaves. This is what mill- 

 wrights call making a hunting cog. 

 Thus, suppose that there are ten leaves, 

 and that the diameter of the wheel is 

 about six times that of the pinion. If 

 this were the exact ratio, there would be 

 just sixty teeth, and after each revolu- 

 tion of the wheel the same teeth and 

 leaves would be continually engaged, 

 each leaf taking every sixth tooth. But 

 if the diameter of the wheel be made 

 somewhat greater than six times that of 

 the 'pinion, so as to admit sixty-one 

 teeth ; then, after six revolutions of the 

 pinion, the first leaf will be engaged 

 with the tooth immediately before that 

 in which it had worked at the com- 

 mencement, and after six more revolu- 

 tions it will be engaged with the tooth 

 before that, or the second tooth from 

 that at which the motion commenced. 

 Thus, it is evident, that the wheel must 

 revolve 61 times, and the pinion 6 x 61, 

 or 366 times before the same teeth will 

 be again engaged. By these means, the 



inequalities of wear arising from in- 

 equalities of form and material will 

 compensate each other. 



(69.) The teeth of the wheel, instead 

 of working in the leaves of a pinion, are 

 made to act upon a form of wheel called 

 ^'lantern, as represented at Jig. 46. The 



T3 



Fig. 46. 



Cylindrical teeth or bars of the lantern 

 are called trundles or spindles. How- 

 ever, notwithstanding the various forms 

 of wheel-work, the principles which we 

 have already explained will always de- 

 termine the relation between the power 

 and resistance. 



(70.) Wheels are denominated spur, 

 crown, or bevel gear, according to the 

 position or direction of the teeth. If 

 the teeth be perpendicular to the axis 

 of the wheel, and in the direction of radii, 

 as in the wheel E, fig. 46. it is called a 



rr- wheel. If the teeth be parallel to 

 axis of the wheel, and therefore per- 

 pendicular to its plane, it is called a 

 crown-wheel. Two spur-wheels, or a 



Fig. 47 



spur-wheel and pinion which work in 

 one another, are always in the same 

 plane, and have their axis parallel. 

 But when a spur and crown-wheel are 

 in connection, their planes and axis are 

 at right angles. By this means, there- 

 fore, rotatory motion may be transferred 

 from a horizontal to a vertical plane, or 

 vice versa. 



When the teeeh are oblique to the 

 plane or axis wheel, it is called a 

 bevellecl-wheel. Two wheels of this 

 kind are represented in/?**-. 48. In this 

 case, the surfaces on which the teeth are 

 raised are parts of the surfaces of two 

 cones. The manner in which these 

 wheels act, and the principles on which 



