Inclined Plane. 117 



. = 50. 



vv 



We know in this case only the quotient obtained by dividing NN' 

 by r i' ; we do not know either the dividend or the divisor. 

 Let us take, therefore, arbitrarily for the divisor v V' a number 

 composed of two factors which shall be neither too small nor too 

 great for the number of leaves to be allowed to the pinions. Sup- 

 pose, for example, v v f 1 X 8 = 56, v being 7, and i>' 8. We 



shall then have ~, = 50, or JVJV' = 50X56. Now 50 and 

 56 



56 not exceeding the number of teeth that can be given to the 

 wheels W and X, I will suppose JV to have 50 ; and consequent- 

 ly those of N' will be 56. If these two factors, or one of them, 

 should happen to be too great, I should decompose them into 

 their prime factors, and see if from the combination of these fac- 

 tors there would not result two smaller factors ; or another num- 

 ber might be taken for v v'. 



Suppose, for a second example, that it is proposed to find the 

 number of teeth and leaves to be given to three wheels and their 

 pinions, in order that while the last pinion turns once in twelve 

 hours, the first wheel shall require a year to make one revolution. 



The common year consisting of 365,25 X 24 X 60 or 

 525949 minutes, and 12 hours being equal to 12 X 60 or 720 

 minutes, it is evident that during one revolution of the first wheel 

 the last pinion will make a number of revolutions expressed by 



JVYW" 

 5 Wo 49 5 we have, therefore, , = 52 T Yo 49 . Let us take 



.AOV./V" 

 arbitrarily v = 7, v' = 8 ; and we shall have - -zss 



or JVWJV" = 5 9 X 7 X 8 v" = 



X 



3681643 v" 

 90 ' 



Of the Inclined Plane. 



196. Jfabody^of any figure whatever, touching a plane Fig 108. 

 XZ in any point C, is urged by a single force, it can remain at 

 rest on this plane only when the direction of this force is perpen- 

 dicular to the plane, and is such at the same time as to pass 



