KINEMA TIC MODELS. 28 1 



absolutely identical with the chain of Fig. 6. The link fixed is the 

 crank, so that, as a mechanism, it is represented by Fig. 9. I am 

 sorry my time will not allow me to prove this, but by analysing the 

 pairs of elements which it contains it shows itself at once. Many 

 other rotary engines of which there are models on the table are of the 

 same kind. Here is one which was exhibited at the Exhibition of 

 1851, and which attracted a good deal of notice at the time Simpson 

 and Shipton's machine. It is really nothing more than the mechanism 

 shown in Fig. 10, although its constructive form so disguises its real 

 character. I might go through a great many more in the same way, 

 but time compels me to leave this part of my subject. 



In Reuleaux's work, to which I have alluded,. and of which I have just 

 completed the English translation, he uses a method which, while 

 it is by no means original with him, has never been formerly developed 

 to the same extent and in the same way. I must try in a few words to 

 indicate the general nature of this method. If we have any plane 

 figure moving in a plane, its motion, at any instant, may always be 

 considered as a motion about one particular point (it may be at a 

 finite or an infinite distance), and this point is called the instantaneous 

 centre, for the motion of the figure. The body may continue to move 

 about the same point, in which case the instantaneous centre becomes 

 a permanent centre ; but in general the motion of the body in 

 successive instants is about different points, each being for the time, 

 the instantaneous centre. The locus of the points which thus become 

 instantaneous centres for the motion of any figure is some curve, and 

 is called by Reuleaux Polbahn, for which I propose the use of the word 

 centroid. If we have any two figures A and B, having a definite relative 

 motion, and make the relative motion of B to A absolute by fixing A, 

 we can, by moving B, find as many points in the centroid as we wish, so 

 to construct the curve. This centroid remains, of course, stationary, like 

 the figure A, and is called the centroid of A. By fixing B and moving 

 A relatively to it, we can in the same way obtain the centroid of B. 

 We have then two curves, one connected with each figure, and these 

 possess certain properties which are of great value in the study of 

 mechanism. As the figures move these curves roll upon one another, 

 and their point of contact is always the instantaneous centre of motion 

 for the time being. It is, of course, impossible for me to prove these 



