274 APPLIED SCIENCE 



the pressures throughout the element. Thus the steam in the 

 cylinder of a steam-engine is a fluid element, and, strictly speak- 

 ing, this element comprises the steam in the pipes and in the 

 boiler, as well as the water in the boiler. Generally, we need 

 only consider the steam enclosed in the cylinder cut off and 

 bounded by the side valve. Wherever discontinuity of motion 

 occurs, a solid element will be considered as terminated or 

 bounded. Thus two rigid bars joined by a flexible tie will be 

 treated as three distinct elements. The flexibility of the tie 

 replaces the sliding motion at a joint which would otherwise be 

 required. The discontinuity of motion here insisted upon as indi- 

 cating the surface of separation between elements is the property 

 by means of which we shall be enabled to determine the relative 

 forces with which separate elements press on one another. Two 

 elements are treated as separate when at any part they are dis- 

 continuous, and also in certain limiting cases when the relative 

 motion at the surfaces of contact is infinitely small. 



The elements of a machine as now defined correspond closely 

 with Professor BEULEAUX' kinematic links. All Professor 

 EEULEAUX' links are elements, but the definition now given of a 

 dynamic element would embrace certain parts of machines which 

 can hardly be called kinematic links, as, for instance, the steam 

 and water mentioned above. Each element of a machine will in 

 what follows be designated by a single small italic letter. 



3. Joints. The name of joints will be given to the surfaces 

 of separation between two elements. When the elements are 

 rigid, joints can occur only where there is sliding or rolling con- 

 tact between the elements. A surface of separation between a 

 flexible tie and a rigid bar will also be treated as a joint, inasmuch 

 as discontinuity of motion may occur at this surface similar to 

 that which occurs at a service of separation between rigid ele- 

 ments. A joint in the sense in which the word is here used is 

 essentially a joint between two elements. There can be no 

 common joint between three or more elements. In ordinary 

 phraseology, we speak of three or more members of a frame as 

 jointed at one place, and speak of the joint there as a single 

 joint, meaning that they all abut against a single pin ; but, 

 in the present paper, each portion of the surface of such a pin as 

 bears against a single element will be spoken of as a single joint. 



