The real points of connection and of difference between them are thus lost, and the subject presents itself to the student as a series—or rather as many series—of interesting problems, which have only a very indistinct relation to each other. He is not led to any standpoint from which he can take a general survey of the whole. For this purpose the apparently simple, but in their results most wonderful ideas of the nature, pairing and inversion of machine-elements and kinematic chains were essential. Rankine unfortunately had no opportunity of making use of these; he does not seem either to have recognised the use of centroids, or the possibility of constrained motion in the higher pairs. He does not even point out that two of the motions of his "primary" pieces are in reality only special cases of the third, the twist, or that the method of instantaneous centres is as applicable to these motions as to more complicated ones. If it had not been for my own feeling as to the value of Prof. Rankine's work, I should not have alluded at such length to what appear to me to be defects or omissions in it. He has done great and lasting service in connection with the scientific study of machinery in this country, and his "Machinery and Mill work" is so familiar to engineers that it appeared to me impossible to leave unnoticed the bearing upon it of Reuleaux's Theory of Machines.
