66 BEYIEWS — ANALYTICAL STATICS. 



mass — then that the unit of mass is chosen arbitrarily — and that 

 when we say that the mass of any body is represented by a certain 

 number, as n, we mean that the body might be divided into n parts, 

 each having the same mass as that which has heen assumed as the 

 unit. This definition of the mode of measuring mass is practically 

 useful : hut whose ideas were ever extended by being informed that 

 the mass of a hody is the quantity of matter which it contains ? We 

 may notice another illustration of the way in which the tendency to 

 formal dogmatic definition has led M. Poisson and his followers into 

 grievous difficulties. It is deemed necessary to define a state of 

 motion — "A body," says Mr. Todhunter, translating Poisson, " is in 

 motion when the body or its parts occupy successively different posi- 

 tions in space." And then, inasmuch as it would be somewhat hard 

 to make this a working definition, the idea of relative motion is in- 

 troduced in the following remarkable expressions : " but since space 

 is infinite in extent, and in every part identical, (partout identique) 

 we cannot judge of the state of rest or motion of a body without 

 comparing it with other bodies, (or with ourselves M. Poisson adds) 

 and for this reason all motions which come under our observation are 

 necessarily relative motions." Now this complicated and objection- 

 able sentence is rendered necessary entirely by the preceding formal 

 definition of motion. Had this been omitted, we should have escaped 

 the difficulty altogether. Thus Poinsot and Duhamel, granting us 

 the privilege of understanding the meaning of the word ' motion,' 

 proceed to explain the terms absolute and relative motion : shew that 

 while we cannot be sure that any particle in the universe is really at 

 rest, we may yet separate the idea of the motion of a particle from 

 the idea of the material body itself ; that we may conceive, that is, that 

 a body might be absolutely as well as relatively at rest ; and thus 

 they come to the definition of force, or perhaps we had better say to 

 the statement in a statical form of the principle of the inertia of 

 matter, viz. that some cause must always be required to produce a 

 motion in a body at rest, and that to such a cause we give the name 

 of force. 



And this will lead us to say a few words as to the grounds upon 

 which theoretical mechanics are or ought to be based. Before we 

 do so, however, we would most seriously protest against any imputa- 

 tion of quibbling or hair-splitting in making these objections to 

 verbal definitions. Such defects are grievous hindrances to the use- 

 fulness of a book, as every one knows who has had experience in 

 teaching. A tutor puts such a book as that of Mr. Todhunter into 



