238 Professor W. E. Dalhij on Vibration Problems. [Jau. 30, 



equations are omitted a solution of the remaining six can be found, 

 and it is such a solution which is the basis of what is known as 

 the Yarrow-Schlick-Tweedy method of balancing an engine. The 

 secondary moments are left unbalanced, otherwise the first two terms 

 in the respective series are eliminated, and the engine is said to be 

 balanced for Primary Forces and couples and for Secondary Forces. 

 A large number of engines have been built on this plan. 



The steam turbine is of course a balanced machine, and its run- 

 ning causes no unbalanced forces to act on the framework. 



A good many marine engines have been built with cranks at right 

 angles, and with their reciprocating masses approximately equal. 



This model is arranged in that way, and its running discloses at 

 once that there is an unbalanced torque acting on the frame. In 

 fact four cranks at right angles is just the one sequence of angles for 

 which it is impossible to balance the reciprocating parts of a four- 

 crank engine amongst tliemselves, even for primary effects. 



[W. E. D.] 



