SECT, vii.] STEAM ENGINES. 235 



between the centres of motion of the beam and the radius bar should be nearly 

 equal to the length of the links. 



494. RULE iv. To find the length of the radius bar when there is no assigned 

 proportion between the length of the stroke and the radius of the beam. 



First, from the length of the radius of the beam, divided by twice the length 

 of the parallel bar, subtract unity. 



Secondly, Find the square root of the difference between the square of the 

 radius of the beam, and the square of the half length of the stroke, and add this 

 root to the radius of the beam. 



Thirdly, Multiply together the numbers so found, and the product added to 

 the length of the parallel bar will be the length of the radius bar. l 



Example. Let the radius of the beam A F be 12 feet, the length of the stroke 

 6 feet, and the length of the parallel bar D G, 5 feet. Then the first opera- 

 tion is, 



12 



2x5 



-1 = 1-2-1 = 0-2. 



By the second operation, the square of 12, less the square of 3, is 144 9 = 

 135, of which the square root is 11-62, and 12 + 11-62 = 23-62. 

 Hence, 



Radius rod = 23-62 x 0-2 + 5 = 9-72 feet. 



This calculation may be much simplified in the following manner. Join A G 

 meeting D B in E ; then since D B, G F, are always parallel during the 

 motion, we have AE:AG:: AB:AF, an invariable ratio ; conse- 

 quently, if E describes a straight line, G will also describe a straight line. 

 But it has been shown that E will very nearly describe a straight line 

 when the segments D E, E B of the link are inversely as the radii C D, 

 A B, or when 



DE:EB::AB:CD. 



But by similar triangles, DE :EB:: D G : A B .-. DG:AB::AB:CD, 



and, 



= . 



1 Where great accuracy of motion is required, diminish in all cases the length of the stroke 

 by its one-sixth part, before it is used in any of the calculations where it is introduced. This 

 preparation will reduce the deviation from a straight line to the least possible amount. ED. 



