108 Prof. T. A. Hearson. [May 30, 



show the likeness and the differences between machines in similarities 

 in the movements or the contrary. 



It is claimed by the author that in those movements the principal 

 feature of a machine resides, distinguishing it from other engineering 

 constructions. 



It is shown that all movements, however complex, are derived 

 from the association together of some of a comparatively limited 

 number of kinds of more or less simple motions, which take place 

 between consecutive directly connected pieces. 



Certain geometrical laws are enunciated, from which are derived 

 the conditions necessary for the association of those motions together 

 in one machine. It is shown that those laws preclude the existence 

 of certajn combinations of motions, and it is suggested that one may 

 be enabled by this analysis to enumerate an exhaustive list of the 

 possible combinations which must include all existing machines, and 

 suggest the design of others not in existence. Moreover, by attaching 

 to each kind of motion a suggestive symbol, a method of expressing 

 the constitution of a machine movement by a simple formula is 

 proposed, whereby similarities and differences between machines may 

 be exhibited at a glance. 



The author commences by considering a very simple mechanism, 

 consisting of four bars united in one continuous linkage by four pins 

 which have parallel axes. By imagining the length of the links to 

 undergo variation from zero to infinity, it is shown that this simple 

 mechanism is representive of all the simple plane mechanisms, and, 

 by imagining other variations to occur, this same mechanism is 

 shown to be representive of still further classes of mechanisms, 

 in which the parts do not move in or parallel to one plane. In this 

 simple mechanism the relative motions of consecutive pieces are 

 either turning, when one piece revolves completely around relatively 

 to the other, the representative symbol being the letter 0, or swing- 

 ing when one piece turns through a limited angle relatively to the 

 adjoining one, represented by the letter U. 



The first law enunciated, which governs the association of the 

 and U motions, is founded on the geometrical fact that the sum of 

 the three angles of a plane triangle is constant, and the sum of the 

 four angles of the quadrilateral therefore also constant. After a 

 complete revolution the angle between the bars is considered to have 

 been increased or diminished by 2fl-. With this extension of the pro- 

 position the constancy of the sum of the angles is unimpaired. 



From this it is seen to be impossible for only one motion to be turn- 

 ing and the other three swinging, otherwise the sum of the four 

 angles would increase or decrease by 2n- each revolution. 



The second law, which governs the association of the motions, has 

 to do with the proportions between the length of the links necessary 



