240 THE DIRECTION OF MOTION. 



of the lines of greatest traction and. least resistance. So far 

 from a cascade furnishing, as it seems to do, an exception, 

 it furnishes but another illustration. For though all solid 

 obstacles to a vertical fall of the water are removed, yet the 

 water's horizontal momentum is an obstacle; and the par- 

 abola in which the stream leaps from the projecting ledge, 

 is generated by the combined gravitation and momen- 

 tum. It may be well just to draw attention to the 

 degree of complexity here produced in the line of move- 

 ment by the variety of forces at work. In atmospheric cur- 

 rents, and still more clearly in water-courses (to which 

 might be added ocean-streams), the route followed is too 

 complex to be defined, save as a curve of three dimensions 

 with an ever varying equation. 



The Earth's solid crust undergoes changes that supply 

 another group of illustrations. The denudation of lands 

 and the depositing of the removed sediment in new strata at 

 the bottom of seas and lakes, is a process throughout which 

 motion is obviously determined in the same way as is that 

 of the water affecting the transport. Again, though we have 

 no direct inductive proof that the forces classed as igneous, 

 expend themselves along lines of least resistance ; yet what 

 little we know of them is in harmony with the belief that 

 they do so. Earthquakes continually revisit the same locali- 

 ties, and special tracts undergo for long periods together 

 successive elevations or subsidences, — facts which imply 

 that already-fractured portions of the Earth's crust are 

 those most prone to yield under the pressure caused by fur- 

 ther contractions. The distribution of volcanoes along cer- 

 tain lines, as Avell as the frequent recurrence of eruptions 

 from the same vents, are facts of like meaning. 



§ 78. That organic growth takes place in the direction 

 of least resistance, is a proposition that has been set forth 

 and illustrated by Mr. James Hinton, in the Medico- Chirur- 

 gical Review for October, 1858. After detailing a few of 



