518 Wisconsin Academy of SciencesArts, and Letters. 
Tliis case is usually a troublesome one to students but bere in¬ 
volves no complexity. Both centrodes vary together as in Fig. 6. 
In Fig. 8, D is held stationary. 
V°B _ab—ad_ 
V°A~ab-bd -Q ° 
that is the Y°B is infinitely greater than that of A, as we have 
here a small centrode rolling up one of infinite radius. Here 
the small centrode though it changes in diameter proves that 
B is always infinitely greater in angular velocity than is A. 
Thus far no really complex case has been taken up, but the 
application of the method will be shown to be as simple as in 
any of those already given. 
Take the complex eight link mechanism, the Peaucellier Cell. 
E'ach link moves with respect to every other one. Usually link 
A is stationary, but it might be desirable to compare the Y° of 
O to that of Ei when F is held stationary. From what has 
gone before we have 
V°C ce—ef 
V°E ce—cf 
C and Ei are therefore rotating in the same direction with 
respect to F about cf and ef respectively. 
Let point n be any extended point in link E, and with a 
known velocity, what will be the velocity of point, m in link C 
when F is held stationary ? 
It may be found by determining from, the given velocity of 
n, the velocity of the point common to the two moving links, ce, 
and from this, the velocity of m, by means of the triangles of 
velocities. 
Take the three links B, D and H, well separated, and let B 
be stationary. Then 
Y°T>_dh—hh 
V°H ~dh=bd 
Here again dh (named from the two moving links D and H,) 
is the point of contact of the two links or centrodes, and the 
points bh and bd are respectively the centers of rotation! of 
links H and D with respect to B. The directional rotation of 
H and I> are opposite—a point not readily seen by imagining 
the links moving about B. 
