270 KINEMATICS OF MACHINERY.
formula, but treating them similarly to the one just discussed, we may write :
(Fx*) for F-,0x
The index X stands as contraction for q x , and is sufficient to make the pairing of C z and F respectively with a liquid quite distinct. For the kinematic chain of Fig. 188 we therefore obtain the concentrated formula (G r C zX F x ), which, as we have seen, serves as well for the water-wheel as for the lift-wheel and the paddle- steamer.
(5 2. Contracted Formulae for Single Mechanisms.
The abridged notation which we have described for kinematic chains cannot be applied to the same chains in the form of mecha- nisms without some additions, for it shows only pairs and not links, and therefore does not in itself furnish any means for indi- cating the fixing of a link. It is, however, most important that we should have the means of extending these concise, and yet for so many cases quite sufficient, symbols to mechanisms.
Although this cannot be done by such logical generalizations as those by which the contractions were arrived at in the first in- stance, still in the chains which are most important to us the end can be obtained by various special means. These means are the giving of definite name-symbols, settled by agreement in each par- ticular case, to the separate links of the chain. If this be done, and the name-symbol of the fixed link, as the one about which something special requires to be indicated, be assigned some par- ticular and conspicuous position in the formula, we have obtained an abridged notation for the mechanism.
We choose the letters of the small Eoman alphabet for the link symbols, beginning with a in each case, and going on as far as may be necessary; the letters indicate in themselves therefore no quality or form. To prevent any confusion arising between these letters and the form-signs, we give the former a specially distinctive posi- tion in the formula ; namely, that of an exponent outside the brackets which inclose the symbols of the pairs. Only one letter,