5S Mr Russell on the Fallacies of the 



effect to a force of three pounds moving a weight of three 

 pounds through a space of only two feet a second ; or that, 

 in calculating the quantity of effective power, a greater ve- 

 locity is equivalent to a greater force. Thus much being 

 premised of the principle of virtual velocities, as apphed to uni- 

 form motions, if we find that, in the case of the crank, the 

 force acting on the piston produces an effect through the cranky 

 in which, although the force may be less, it is exerted through 

 a space equlvalently greater than that through which the piston 

 is moved, then we have a right to infer that there is no loss of 

 power, but that what is lost in force is gained in velocity. Now, 

 this is precisely the case. 



While the piston moves through the length of the cylinder, 

 which is equal to the diameter of the crank circle, it moves the 

 crank through the circumference of a semicircle ; now, the 

 length of the diameter is to the length of the seniicircumference 

 as follows : Diam. : — semicirc. : : 2 : 3.14159, being a little 

 more than the ratio of 63 : 100. 



If, then, we find that the mean force exerted through the 

 crank is not less than in this proportion, we shall be able to 

 shew that the loss is imaginary. Now, the mean force on the 

 crank obtained from the third column of the preceding table is 

 also 63 to 100 ; that is to say, the force in the piston is greater 

 than the mean force in the crank hi precisely the same ratio in 

 which its velocity is less than it. 



There is another view of the matter to which I would direct 

 particular attention. It is said that, at the top and bottom of 

 the stroke, the position of the crank is so unfavourable to the 

 production of circular motion, that no force of steam, however 

 great, would produce any good effect towards causing revolu- 

 tion. This leads me to trace the progress of the steam itself in 

 the cylinder, in connection with the motion of the piston and 

 of the crank. 



The steam, when the piston is at the top of the cylinder, has 

 not yet been admitted to press upon the piston, and, therefore, 

 none of its foi-ce can at this moment be lost. On the instant 

 of leaving this point, the steam enters, and at the end of the first 

 18°, presses round the crank with a force of only 12.80 per 

 cent. ; but let it be observed, that the steam only carries the 

 piston through a space of about l-8th part of that through 



