COMPOSITION OR AGGREGATION OF FORCES IS A CONSEQUENCE. "^Qd 



treatise on geometry half apologises for considering an angle as a magnitude, and informs the 

 reader that it "may not improperly be considered" as a magnitude. And this at two thou- 

 sand years from the time when Euclid showed how to take any given angle two, three, four, 

 &c. times, and, which is more to the purpose, established ratios of angles. Belief, short of 

 certainty or not, is nearly established as a magnitude; probability, now fully recognised, be- 

 gins to be seen to be belief under another name. Curvature is as yet hardly recognised, but 

 is on its way: the same may be said of velocity, not as a measure, but as a thing measured. 

 Momentum and moment of rotation, the first of which might more properly be styled moment 

 of translation, when compared with the second, are still, in elementary writings, introduced as 

 numerical formulae derived from the relations of other things, and not as things. As mind pro- 

 gresses, magnitudes now unconsidered will be gradually received, with the slowness which 

 marks all changes of thought. 



5. Statical pressure. The effort which would, if unopposed, produce motion, but which 

 by counteraction does not, has had various demonstrations of the law of aggregation proposed, 

 and objections have been offered to every one of them. On the one hand the dynamical proof 

 has been condemned because it introduces into statics the consideration of velocity: on the 

 other hand, many have been puzzled by finding that the thing which, by its very definition, 

 tends to produce motion, is reasoned on, not merely without reference to the idea of motion, 

 but under a compact that any introduction of the idea of motion would be out of place. The 

 statical proofs, as they are called, have failed to establish full confidence in themselves: I sup- 

 pose the reason to be that they do not clearly enunciate the physical grounds on which they 

 stand : they seem to be all geometry and no physics, as if the law of aggregation of pres- 

 sures were a result of thought. And a result of thought it is declared to be in an excellent 

 manual of physics which I have lately seen. The preceding part of this paper will, it seems 

 to me, establish all or most of these proofs in perfect rigour, as a consequence of definite pos- 

 tulates ; it remains to examine here how far these postulates contain results of experience. 



Pressure and velocity, two magnitudes derived from different senses, touch and sight, may 

 each be conceived independently of the other. We can imagine, without contradiction, think- 

 ing beings who have never seen motion, but have never passed a moment without feeling 

 pressure : we can also, with equal ease, imagine other beings who have constantly seen motion, 

 but have never felt pressure. Our sensations of pressure, and our physical knowledge of it as 

 a cause of motion, institute a connexion between the two which we cannot get I'id of, when 

 thinking of ourselves. Our examination of the postulates relative to pressure will require us 

 to put ourselves in the position of beings who want the sense of touch. 



(1) Two pressures can aggregate into a third, distinct from either. Is this knowledge 

 wholly a result of thought ? That two magnitudes put together make a third is a result of 

 thouglit in every case in which thought holds the parts and the whole in joint and separate 

 existence at once: as when two lengths AB, BC, make a third length AC. But two pressures 

 in the same direction, and their sum, are not held in joint and separate existence at once : we 



