DUNCAN, DAVIES, GOSSAGE. 391
serve in any case only for pumps working against a very small head. Practically the whole construction is worthless.
Chamber-gear from the Conic swinging Cross-block.
The swinging cross-block ( 0-^0*-)* gives us results which do not differ kinematically from those furnished by the turning double- slider (C-^C L -) d . This has been already shown in 75. Here, however, I have separated the two classes of mechanisms, for this enables us to arrive more naturally at the three following machines, which are indeed almost literally inversions of those which we have been considering.
Fig. 1, PL XXIX. in the first place, which is given only to make the nature of the others more intelligible, is a simple inversion of Fig. 1, PI. XXVIII. ; b is fixed, the chamber d moves upon it, a turns about 2 instead of about 1 ; the block c is placed as a packing-cylinder in the slot of the disc I. The figure will help to explain that of Duncan's machine* Fig. 2. In it b is again the fixed link, but the piston disc has taken the form of a double cone, and the chamber is made spherical. The revolute 1 of a, which in. the last figure is a simple cylinder, is here the double cone ; its axis is A A, which is caused by the link d to oscillate exactly as in Fig. 1. The block c might be arranged so as again to form a packing -cylinder, having a perpendicular axis in the centre of the partition in b. Duncan appears, however, to have used hemp packing.
Fig. 3, PI. XXIX. shows a construction in which the crank of Fig. 2, or rather of Fig. 1, is replaced by a very much less advan- tageous arrangement. It was proposed by Davies in 1837, besides the pump we have described (Fig. 5, PL XXVIII.), and the addition consists of a cylinder pair, and four spheric pairs, that is of a chain (C 6r 4 ), replacing the crank. A patent was taken out in France in 1838, by Gossage,t for a very similar arrangement, which was
- Clark's Table of Mechanical Motions, Nos. 61 and 62.
f Propagation Industrielle, vol. iii., 1868, p. 246.