Page:The Kinematics of Machinery.djvu/291

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we must substitute -j- for V~. The constitution of this mecha- nism is the same as that of the lift- or flash-wheel. If we suppose the link Q\ . . . . Q\ fixed instead of the link V~ ... -f- ... C~, we obtain a very different but very familiar mechanism. The link V~ ... + ... C~ moves in the (relatively to it) stationary water: the mechanism is that of the paddle-steamer. It will be seen that in this case we must presuppose that the link c possesses the requisite buoyancy.

FIG. 188,

We may here also use the abridged notation. In the first formula the pair C f ,P z presents a certain difficulty, for it is our object if possible not to use two capital letters in the contraction for one pair of elements, in order that there may never be any doubt as to whether each letter stands for a pair or not. So far as it is possible we wish that the number of capital letters in any con- tracted formula with the addition of course of the repetitions, if any, indicated by the suffixes shall show at once the number of pairs in the chain for which the formula stands. We must for this purpose have recourse to a convention. Without leading to any misunderstanding we may denote the pair C Z ,P Z by the sym- bol ((7 Ip ), and by doing so we obtain as an expression for the whole chain : (<7 tf lp P+). We add the sign -f (" crossed ") to the symbol (P) of the sliding pair, so as to make the position of that pair quite determinate.

Similar difficulties as to double letters occur twice in the second