The higher pairing which occurs here receives further consideration in Chapter XIII. § 157.]
56 (P. 498.) [The matter may also be looked at in a somewhat different way. The driver of the old engines formed an element of a sliding-pair, as it does still, for instance, in direct-acting pumping engines. The attempts at rotary engines seem to me attempts to replace this sliding-pair directly by a cylinder or turning-pair. Something equivalent to this is very frequently insisted on in descriptions and specifications, and has certainly, in a more or less indistinct form, been present in the minds of many inventors, who have persistently refused to see more than one moving part in their machines. It is one of the results most to be hoped from the acceptance of Professor Reuleaux's method of analysis, that the energies of these and other ingenious minds may be turned into worthier channels.]
57 (P. 522.) [§ 137, as it appears here, is a summary of a much longer treatment of the subject given by Reuleaux, which I hope may be published at length in another form. He discusses in some detail the present position of workmen on the Continent, and the way in which they have been affected by the machine and machino-facture. The circumstances of the case, as he describes them, differ in some very important respects from the circumstances attending similar industries in this country.]
58 (P. 533.) [It will be remembered that strictly the pair () is not closed, for it has not of itself the cross profiles necessary to prevent axial motion. This is_a general difference between the pairs formed from and those formed from ; the former may be made completely constrained in themselves, while in the latter (as Figs. 363 to 367 for instance) the necessary constraint in one or more directions is obtained only by the use of pair-, chain-, or force-closure. This closure being provided, however, the form of these higher pairs determines motion as absolutely as the closed forms of the lower ones.]
59 (P. 538.) [A comparison of this table with that given at p. 543 of the German edition will show some points of difference between the two. These appeared to me necessary to bring the table and the text into complete agreement,—especially as several corrections (see Preface) have been made in the latter,—but it is right to say that I have not been able to submit them to Prof. Reuleaux, who was on his way to Philadelphia when they were made. For my own purposes I have used a different classification, which I need not give here. There is one detail connected with the notation of the higher pairs which might be modified, I think, with advantage. Prof. Reuleaux uses, e.g. the symbols () and () for different pairings of with . The first form appears to me much the better, so that I would suggest the use of (), () and so on, instead of (), (), etc. It would then be understood that a small letter used simply as a suffix indicated some quality of the element denoted by the capital letter after which it was placed, and possessed in common by the two elements of the pair, while if a stop of any kind (comma, semicolon, etc.) were marked between the two letters the meaning would be that the pair consisted of two dissimilar elements, paired in the manner pointed out by the stop. Thus (), or more strictly (), would indicate a pair of elements each of the form , while () would be a pairing of with , etc.]
