ON THE GENERAL THEORY OF THE STEAM ENGINE. 181 



and these occur in the positions represented in the figures annexed. For only one engine 

 and crank we have before found the greatest deviation from the mean angular velocity to be 



_ ( -B + 0'207 ) in which, for the moment, M r e accentuate the symbol P, because in this 



M () \ 4 r * 



case it represents the entire acting power, whereas in (25) it represents only the power of one 

 of the two engines ; and, under like circumstances, we have P' = 2 P, so that the latter ex- 

 pression becomes ^ ( - + 0'414 j. Comparing this with (25) it appears that the 

 variation of velocity with a single engine and one crank, and the variation of velocity with a 



pair of engines and two cranks, are to each other in the ratio of - + 0-818 to - + 0-082, 



r r 



which ratio varies from about 3 to 1 up to that of 10 to 1. 



These results are of much value in pointing out the effects to be produced by varying the 

 radius of the crank, the length of the stroke, and the diameter of the cylinder. All other 

 circumstances being the same, the values P p, M, (to) will be constant ; and therefore the 



extreme variation of velocity will always be proportional to + 0'828 for one crank, or 



P + 0-084 for two cranks acting alternately in the usual way. Hence it follows, that by 

 r 



diminishing the radius of the crank and increasing the length of the connecting rod, the 

 irregularity of the movement will be materially diminished, more particularly when two 

 engines are employed. It is on this account highly desirable to have as long a connecting 

 rod as convenient, in proportion to the radius of the crank ; while, on the other hand, it adds 

 another to many important objections 1 against the adoption of the American proportions 

 recommended by Professor Renwick at page 109, viz., to employ a crank of large radius and 

 a long cylinder, since the disagreeable and destructive jolting, experienced in the working of 

 engines, is principally due to the irregularity of action here alluded to. 



We have gone thus far into an investigation of the motion of the crank, as it forms one of 

 the most important instruments of the steam engine, and has hitherto met with very little 

 attention from scientific writers. It is, doubtless, the most simple, and perhaps the most 

 efficient, contrivance that can be devised to convert a reciprocating action into a rotatory 

 motion ; and in this respect we cannot be surprised that it has not been superseded by any 

 one of the numerous inventions that have been proposed with the view of dispensing with it. 

 We are compelled, however, at the same time, to admit that this beautiful simplicity is 

 accompanied by corresponding inconveniences in the inequalities of motion, pressure, friction, 

 and consequent wear. The mechanical defects of engines constructed on the rotatory 

 principle appear to be of greater magnitude, and the disadvantages and difficulties that stand 

 in the way of their application to the most important uses, are of a very formidable nature. 

 This is much to be regretted, as we conceive a perfectly equable motion to be a great deside- 

 ratum in the steam engine, and the only hope we can have of succeeding in obtaining it is in 

 the exclusive employment of rotary action. On this head we may refer our readers to an 

 instructive paper, entitled " On the Fallacies of the Rotatory Steam Engine," by John Scott 







1 See pages 365, 366, of the present work. 

 2 a 



