608
�NOTES.
�or, again inserting the quantity represented by A :
�cot y =
�1 cos* a sin? <o sin* a sin* a cos* a>
�cos a sin a
�cos a sin a
that is, cot y = tan a cos* a>.
a relation which also may easily be determined graphically, as is shown, for
�example, in Fig. 452. It gives the ratio
�x
- !
tan a
�that is, x cot y.
���FIG. 449.
62 (P. 400.) It is not difficult to add new forms synthetically to the many old ones which we have mentioned. Indeed, the foregoing investigations permit such problems to be given directly as exercises in a course of machine instruction. I do not intend to urge here the use of such exercises, which would be suitable only for very advanced students ; they do not, however, essentially differ from those of modern chemistry, where the more advanced students in the laboratory are exercised in the synthetic development of new series of bodies. [I venture to go further in this matter than Prof. Reuleaux, and to hope that synthetic exercises may become both possible and popular among our students to a considerably greater extent than he suggests. The formation of chamber-trains alone gives immense scope for such exercises, and there are also other directions in which they could be worked without touching on problems of any serious difficulty. I know no kind of exercises which are likely to excite so much interest among the class of young men who in this country devote themselves to the profession of engineering.] I may give an example of this. It will be noticed that in the twelve conic chamber-trains formed from (Cjf C*-) d and (C^ C 1 -} b the chambering (F : F)=c, d is never used. This, might, however, be done as follows. Instead of making the element 4 of the link d into a diaphragm and guide for c (as in Fig. I., PI. XXVIII.), it might be formed into a sector of a hollow cylinder with cylindrical openings at its ends, as in Fig. 450. In the chamber thus formed, the cross-section of which is similar to that of the former spheric-sector cham- bers, the element of c belonging to the pair 4 may be placed as a piston. This takes the form of a slice of the same cylinder, fitted with a shaft, the ends of which might project beyond the chamber. To these projecting ends an outer frame is fastened, which carries the cylinder, <7+, of the pair 3 belonging to the link c. The link b has open cylinders both at 2 and at 3, and is simply a connecting-rod with its two open elements normal to each other. At 2 it is
�
