FAEMEES' INSTITUTES. 153 



grease is ii positive disadvantage, as tlio grit adheres to the teeth, thus Avearing 

 them very fast. Where there is no grit grease does no hurt, but it is at the 

 same time an expensive hixury, as it does no good. "With wheels properly con- 

 structed there is no slipping of the teeth on each other, and no sliding friction. 

 Wheels -whose teeth need to be greased in order to run smooth, arc faulty in their 

 construction, and should be avoided, as they indicate poor workmanship through- 

 out the whole machine. 



Worhnanshij) and Material. 



Perhaps no one thing is of more importance in determining the utility and 

 durability of a machine than good workmanshi]). A conception absolutely per- 

 fect can result in nothing but a total failure if constructed by a bungling 

 mechanic. With poor workmanship, the axles chuck and slip in their boxes, 

 producing a tremendous waste of power. Tlie same effect is produced by allow- 

 ing nuts to loosen Avhen working machineiy. 



Here is an apparatus designed especially to illustrate that j)oint : You observe 

 how easy it moves when the nuts are tight, and there is no slipping at the joints. 

 But now let me loosen this nut: 3'ou see the difference at once. It requires so 

 much force that I can scarcely move it, and very forciljly illustrates the need of 

 close joints and tight nuts. 



Another thing of great importance is the shape of the teetli in the cog-wheels. 

 We perhaps will find more machines working hard from this one cause than 

 from any other. Very frequently the tooth of one wheel will strike the tooth of 

 another, pull steadily for one instant, rub and slide tlie next instant, and so 

 continue until the whole machine groans and trembles. Witli teeth of such 

 construction, grease could be used with positive advantage. 



Teeth constructed as they should be wear equally m all parts, and each tooth 

 hits its mate fairly and squarely, has no sliding motion upon it, and leaves it 

 without a jar. The method of forming these curves of the cogs or teeth is quite 

 complicated, and is founded on the following principle : 



If a wheel were to roll on a board or other level piece, each point would 

 describe a curve ; starting at the bottom when the wheel commences to roll, it 

 rises to the top of the wheel when it has turned half way around, and again 

 sinks to the bottom when the wheel has turned clear around. This curve is 

 oalled the cycloid, and is one on Avhose mathematical properties many an 

 examination pony has been ingeniously composed and gallantly rode by the 

 student of mechanics. 



If we curve the line so that the circle rolls on the outside of a circumference, 

 we shall have a similar curve called tlie epi-cycloid. If, on the other hand, 

 we curve the base line so that it is concave toward the circle, the cycloid is 

 varied somewhat in form, and is called the hypo-cycloid. 



Now you saw that the cycloid was made by a wheel rolling on a straight line. 

 The case corresponding to this in machinery is the ordinary rack and pinion ; 

 and we farther notice that if this curve is not given originally to the teeth of such 

 wheels, they will soon wear into tliat shape. 



In case of two cog-wheels working into each other, the curve becomes very 

 much more complex, for in that case we have one wheel rolling on another, and 

 ,also rolling inside another.; and we find that the face or point outside this line 

 called the pitch line, is epicycloidal, while that inside this line is a portion of a 

 hypo-cycloid. It is to be noticed that these curves are not made by the pitch 

 -circles of the wheels, but by two imaginary equal circles. 

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