318 KINEMATICS OF MACHINERY.
men, or in the clumsier form of Fig. 248 employed for drawing on
plaster;* and so on. Its special formula is (C" 2 'P^)a. The connec- tion between this mechanism and the last which we call the in- version of a chain was dis- covered by Chasles, as I have already mentioned in a note to 3 ; he missed, however, the principle really underlying it.
The chain (O^P^) is, as we 248 have seen, frequently used in
machinery. Its real nature,
however, is even more hidden than that of most chains by its constructive form ; and on that account its real connection with other chains has hitherto remained unrecognised.
?3. The Crossed Slider-crank Chain, (CJ P+).
The very considerable number of forms in which we have now seen the quadric crank chain by no means exhausts it, for in the slider- crank chain (C^P- 1 -) and those derived from it it is always possible to make a difference in length between the infinitely long links. By using different points in our mechanism as starting points, as it were, for the infinite lengths, we can make between these a finite difference of any desired magnitude. We shall very briefly consider the alterations which can thus be made in the chain.
If in the crank chain ((?), Fig. 249, we make the link c in- finitely long, and therefore at the same time make d infinite, but arrange them so that c be longer than d,-\ we obtain the chain shown in Figs. 250 and 251. The direction of motion (relatively to d} of the pin 3 no longer passes through 1, but at a distance from it equal to the finite difference between c and d. We shall call these
- Called in Germany StucLateur-zirTcel, and in France also Compas de menuisier.
t Perhaps it would be better to say rather that the links are so arranged that if their point of intersection were at any imaginable finite distance, c would be longer than d.
