354 KINEMATICS OF MACHINERY.
steam-pipe with it above the latter. In both cases the force- closure of the block was effected by its own weight. The higher pairing between a and c is badly suited for making the steam-tight joint which is there required.
We see now what has not previously been recognised that these eight chamber-crank trains are all founded upon the familiar mechanism of the first example, and are all derived from it in the same way, by forming two of its links so as to serve as chamber and piston respectively and by the addition, where necessary, of valve gear. We shall not here enter further into the question of the practical value of any of the machines ; apart from this, however, all the eight solutions are equally legitimate, and there- fore merit equal attention from our present point of view. The links which are used as piston and chamber are
c and d, b and d, a and d.
In every case d is the chamber. This is a very natural choice, for d is the fixed link and the necessary steam or water pipes can therefore be much more easily connected with it than with any of the other links. We shall, however, soon see that in spite of this advantage one of the moving links has not unfrequently been chosen in practice as the chamber. The illustrations which we have given, therefore, do not nearly exhaust the varieties of chamber-crank gear which can be formed from the mechanism (C' 3 'P- L ) d , there would be no difficulty in arranging other combi- nations. There could hardly be machines having less apparent resemblance to the simple crank chain than those of Lamb they appear at first to have nothing in common with it ; it may even be difficult for the reader, until he has become more familiar with the methods of kinematic analysis, to realise their identity. Not- withstanding this our analysis has led us to the result has shown us distinctly the real nature of the machine without any forcing or special assumptions whatever. This example serves to show too how necessary our former general investigations were, how important it was for us to become familar with the exchangeability of -j- and in the lower pairs, the expansion of elements, the reduction and augmentation of chains and so on, and to be able to recognise the effects of these processes upon the external form of the mechanism.
