1847.] WHEWELL ON THE WAVE OF TRANSLATION. 231 



But we may put this result in a shape more readily conceivable. 

 It is equivalent to 4500 cubic miles of water raised through a space 

 of J^ of a mile ; or again, to a body of water 45,000 miles in sur- 

 face and ^ of a mile deep, raised through ^ of a mile. If then we 

 suppose a sea-bottom 450 miles long and 100 miles broad, which is 

 3^ of a mile below the surface of the water, to be raised to the surface 

 by paroxysmal action, we shall have the force which we require for 

 the distribution of the northern drift, on the numerical assumptions 

 which have been made. And this is true, whether we suppose the 

 elevation to have taken place at once, or by repeated operations, so 

 long as they are paroxysmal. We shall have the requisite force, for 

 instance, if we suppose this area to be elevated by ten jerks of 50 

 feet each, fifty jerks of 10 feet each, or by the same 500 feet any how 

 divided into sudden movements. And as we diminish the area ele- 

 vated, we must increase the total amount of elevation in the same pro- 

 portion, so as to retain the same ultimate product of water paroxys- 

 mally elevated through a certain space. In all these cases, we shall 

 have a machinery, which, operating through waves of translation, will 

 produce the requisite effect. And if any of our data be held to be 

 erroneous ; — the area occupied ; — the amount of matter in the drift ; — 

 the amount of friction or tenacity to be overcome in propelling it ; — 

 the law of its diminution in quantity as we recede from the centre of 

 distribution ; — the final result will have to be proportionally diminished 

 or augmented. 



It may be asked whether, since the paroxysmal elevation may thus 

 be reduced into successive smaller elevations, the same result would 

 not follow if it were so reduced as to become, not paroxysmal, but 

 gradual, and even insensible : for, it may be said, mechanical power 

 retains its amount however much it be thus distributed through time, 

 and divested of the character of extraordinary violence. And to this I 

 reply, that no action except such as is of a paroxysmal character could 

 produce the effect. This impossibility depends upon the nature of 

 the effect to be produced. The friction of the bottom which supports 

 the drifted materials, and the tenacity of the masses, are to be over- 

 come : and the peculiarity of such resisting forces is this ; — that 

 except the force which acts be sufficient to overcome these resistances, 

 it produces no effect, and is altogether lost. If we push at a mass 

 resting on the ground, with a force insufficient to move it, the force 

 which we exert is wasted, and disappears from all calculations which 

 suffer force to be preserved and transferred into the change produced. 

 A very small elevation, even if sudden, would produce a wave of 

 translation which would pass over all the large masses, and leave 

 them unstirred ; and the wave would disappear without producing 

 any such effects as we are here endeavouring to account for. 



And thus, the great mass of northern drift, inasmuch as no con- 

 siderable part of its transfer can be accounted for by any minute 

 causes or languid operations of water, is an irresistible evidence of 

 paroxysmal action ; and of action in a scale which may be judged of 

 from the conclusion at which we have arrived : — an elevation of 45,000 

 square miles of sea-bottom through 500 feet. And this conclusion 



