ON AMSLER'S PLANIMETER. 



403 



on tho cylinder being caused to traverse from x to y, the motion will be one 

 compounded of rolling and of sliding ; the trace will still be made on the 

 cylinder ; the length of that trace will be, as before, the length x y, but the 

 trace will now be a spiral, which may be developed into the triangle x y z, 

 and the base x z will bear such a relation to the hypotenuse x y as the 

 base m n of the triangle mno bears to the hypotenuse n o. But it has been 



Fig. 2. 



said that in the journey from x to y the cylinder will have had a motion 

 compounded of sliding and of rolUng; the extent of the rolling will clearly 

 bear that proportion to the total traverse x y that the base m n bears to the 

 hypotenuse n o ; and this proportion may obviously be any thing between the 



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