234 OF THE PARTS OF [SECT. vn. 



as negative in the calculation, when the radius bar is to be less than the parallel 

 bar. 



This expression, which will be found to be of important use in rectifying and 

 adjusting the motions of old engines, and indeed in all cases where it may be 

 necessary or desirable to have the radius bar to work from a stated centre, was 

 first investigated in the valuable treatise on ' Mechanics for Practical Men,' by 

 Messrs. James Hann and Isaac Dodds, (Newcastle, 1833,) a work in which mathe- 

 matical theory and useful practice are combined throughout, with remarkable 

 clearness and simplicity. 



If the beam from the centre of motion to the point F be one and a half times 

 the length of the stroke or b = 3 s ; then, 



r = +V2 ( 3 *- 2c ) +c = 2-9142 *_(8-8c) + c . 



In any case, except when the radius bar C D, and parallel bar D G are of the 

 same length, the deviation is increased by increasing the quantity of angular 

 motion of the beam. Hence, beams having short parallel bars should be limited 

 in the extent of angular movement ; indeed the motion should not in general 

 exceed 20, and thjs is very nearly the case when the distance of the end F of the 

 beam from its centre of motion A, is to the length of the stroke as 3 : 2 ; in 

 such case the radius bar may be found as follows : 



493. RULE HI. To find the length of the radius bar, when the length of the 

 beam from the centre of motion is to half the length of the stroke, as 3 to 2. 

 From three times half the length of the stroke subtract twice the length of the 

 parallel bar, and multiply the difference first by the half length of the stroke, and 

 then by the number 2-914. Divide the product by the length of the parallel bar, 

 and the quotient added to the length of the parallel bar will be the length of the 

 radius bar. 



Example. Let the length of the stroke be 8 feet, its half 4 feet, and let 

 the length of the parallel bar D G be 3 feet ; then 3x 4 2 x 3 = 6 ; and 

 6 x 4 x 2-914 = 69-936, which divided by 3 gives 23-312 ; add to this the 

 length of the parallel bar 3 feet, and we have 23-312 + 3 = 26-3 12 feet, for the 

 radius bar C D. 



A short parallel bar is assumed in this example, to show the great length of 

 radius bar required in such a case. 



The length of the links D B, G F, are from four to five-tenths of the length of 

 the stroke, depending on convenience and space ; but the longer they can be made, 

 the less oblique strain will take place during the motion. The vertical distance 



