LESSONS IN GEOLOGY. 



line A r, but along any other tangent to the large circle, the per- 

 pendicular from thi! fulcrum o on it* direction would (till be the 

 radio* of the wheel ; and, by the general principle of the lever 



established in this lesson, the power and 



resistance would be still invertely a* the 



radii of wheel and axle. 



A treadmill, used for punishment in prison*, 



4 > 1">"1 B I is another instrument of this kind, the power 



{ I being the weight of the prisoner* ascending 



l\ J the steps placed on the outside of the wheel, 



I N^^ j/ and the resistance the weight of the water 

 Q ~~ w pumped, the corn ground, or other work done. 



P {tt The windlass is another, turned generally by 



p. M a winch handle, and used to raise water from 



wells, or lift goods into stores. In Fig. 21 

 (page 152) the reader will find an example of the utility of the 

 wheel and axle as a mechanical power in the crane, by which two 

 men, by turning the winch-handle attached to the axle, are able 

 to lift o horse out of the steamer alongside of the quay. 



A particular form of the windlass, which was first invented in 

 China, and which may therefore be called the " Chinese windlass," 

 ia given in Fig. 65, where only the axle is represented, consisting 

 of two ports, one thicker than the other, but both forming one 

 solid piece. The winch handle, 

 or wheel, is to the right con- 

 nected with the larger axle. The 

 weight to be raised is suspended 

 from a hook attached to a pul- 

 ley, round which the lifting rope 

 passes, one part winding round 

 the thick axle while the other 

 unwinds from the thin. The 

 weight with each turn of the 

 wheel ascends by the difference 

 between the length of the rope 

 that winds and unwinds, that 

 is, by the difference between 

 the circumferences of the 

 two axles. Moreover, since 

 the weight is equally divided 

 between the two ropes which 

 ascend from the pulley, the 



Tig. 65. 



force acting at the circumference of each axle is half the weight. 

 It is evident, moreover, that the power applied to the winch 

 handle has to balance the difference of the actions of these 

 forces at the axle, or the moment of the power must be equal to 

 the difference of the momenta of these forces. But each force 

 being half the weight, its moment is half the weight multiplied 

 by the radius of the axle at which it acts ; and therefore their 

 difference is equal to half the weight multiplied by the difference 

 of the radii of the axles, or, which comes to the same thing, 

 to the weight into half the difference of these radii. But the 

 moment of the power being that force into the radius of the 

 wheel, we immediately learn that 



In the Chinese windlass the power multiplied 

 by the radius of the wheel is equal to the resist- 

 ance multiplied by the difference of the radii 

 of the axles. 



THE COMPOUND WHEEL AND AXLE. 



This is a combination of wheels and axles, of 

 the kind already explained, made for the same 

 purpose as the similar combination of levers in 

 Lesson IX., namely, the mechanical' advan- 

 tage of a multiplication of the effect of the 

 power. The wheel and axle being once clearly 

 understood to be a lever, there con be no 

 difficulty in extending the rule which holds 

 good of the compound lever to this combina- 

 tion. In Fip. 66 is such a combination. By 

 cogged teeth the axle of each wheel works on the circumference 

 of the next succeeding, the power, P, being applied by a &* to 

 the circumference of the first wheel, which does not requir^Blh. 

 It is evident that, as explained of the compound lever, the condi- 

 tion of equilibrium must be that 



In the compound wheel and axle, the power is to the resistance 

 as the product of the radii of the axles ia to the product of the 

 radii of the wheels. 



Fig. 66. 



LESSONS IN GEOLOGY . 



ATMOSPHERIC, ORGANIC. AUD CHEMICAL AOEHCIES. 



TBI direct action which the atmosphere exorcise* ia UM altera. 

 tion of the earth's crust is through the agency of wind. Tim 

 atmosphere aUo act* widely and continually upon rock*, attack- 

 ing them chemically ; hot this motion most U reserved for iU 

 proper place. The power of wind can only be felt by movable 

 particle* that is, by sand. As the wind* sweep orer tb*> 

 deserts, they urge before them cloud* of fine *and, which drift 

 here and there, continually altering the feature* of the land* 

 scape, and extending the detest domain by covering the fertile 

 tract* which border on the sandy waste. Bat the change* which 

 occur in such region* are of little or no moment, for the ab- 

 sence alike of water and vegetation preclude* the possibility of 

 these sand-hill* ever becoming fixed. Bat thi* i* not the oa*e 

 with that belt of sand which line* the ooa*t* of many maritime 

 countries. Here considerable and permanent change* are effected 

 by the alteration of the sand dunei by the wind. The shore* of 

 the Bay of Biscay are celebrated for these dune* ; the wind blow* 

 the particle* of sand over the erect of the hill in constant 

 succession, and thus the hill is moved- The done* of Biscay 

 often advance sixty or seventy feet in a year, covering with irre- 

 sistible encroachments farm* and villages, and are sometime* a* 

 much as 300 feet high. In many part* of the world thi* procee* 

 is in action. When a covering of vegetation spring* up on the 

 surface of the hill, all further advancement i* prohibited, and 

 the dune becomes permanently fixed. Such hill* are distin- 

 guished by the name of sub-aerial or jF.olian accumulations (so 

 called from JEolus, the god of the winds, according to the old 

 Greek and Roman mythology). 



Frost is generally reckoned an atmospheric agent. It* power 

 is very great, and it would be difficult to limit the geological work 

 it effects. "When water freezes, at the moment of it* solidi- 

 fication it expands, with an almost irresistible force, one-tenth of 

 its volume that is, ten measures of water, when frozen, would 

 become eleven measures of ice. The first frost of winter 

 solidifies all the particles of water with which the rock* are 

 soaked, forcing the particles of rock from each other, and when 

 the thaw comes, much of its surface crumbles down. Thi* action 

 is not very visible, because the rain easily transport* the fine 

 particles thus separated from the moss. Yet when we consider 

 the vast surface which is annually exposed to a temperature below 

 freezing point, we shall have some idea of the great effect which 

 frost has in assisting the general degrading action which the 

 surface of the earth is ever undergoing ; and our estimate will 

 be increased when we know the force which is exercised by the 

 solidifying ice. If a hole be bored in a cannon-ball, then filled 

 with water and plugged with a fine-threaded screw, upon causing 

 this water to freeze by immersing the ball in a freezing 

 mixture, the expansive force will be found sufficient to break 

 the ball. In the Canadian forests, often the stillness of the 

 night is broken by a loud report, as some giant tree is rent by 

 the united power of the watery particles expanding on their 

 solidification, under the influence of the first frost of winter. 



Frost also acts geologically by means of avalanche*, glacier*, 

 and icebergs. 



An avalanche does not play a very prominent part, seeing the 

 sphere of its action is very limited. When large masses of ice 

 and snow collect on the inaccessible heights, and become either 

 overbalanced by their own weight, or loosened by the warm 

 sun of the spring, the mass foils into the ralley beneath, bearing 

 with it rocks, etc. ; and the traveller, as he passe* through the 

 mountain vnllcys in Switzerland, often finds piles of delnris which 

 have been brought down by an avalanche from the height* 

 above. This the valley stream carries down into the lake oc 

 river, and thus material from the summit of the chain mingle* 

 with the sediment which the stream erodes from the valley 

 through which it passes. It occasionally happens that an 

 avalanche in its fall dams up the channel of a stream ; the pent- 

 up waters gather in great volume, and at last burst their 

 barrier, ploughing the valleys in their course, thus doing great 

 geological work. 



Glacier* are some of the most interesting feature* of Alpine 

 scenery. They are, in fact, river* of ice, not frozen rivers, 

 but vast quantities of ice, which is formed amid the eternal 

 snows, and by a peculiar motion, known as that of a VIKCOU* 

 body, descends down the valleys until it reaches such a point 



