SOURCES OP POWER.] 



APPLIED MECHANICS. 



817 



In practice, no material error will arise from the 

 , assumption of the simple law we have already stated 

 j and if strengths to resist shearing be calculated according 

 I to it, let the mechanic, as far as he can, contrive to brint 

 the shearing strain against the greatest depth, and he 

 will certainly be safe against fracture from this cause. 



In punching a hole in metal, the surface of the separa- 

 tion produced, is the circumference of the hole, multiplied 

 by the thickness or depth ; and the resisting force should 

 be equivalent to the tensive strength of a bar of the same 

 material, having a sectional area equal to the surface of 

 separation. Thug, in estimating the force required to 

 punch a circular hole, 1 inch in diameter, through a 

 | plate of malleable iron Jths of an inch thick, we should 

 reckon the circumference of a circle 1 inch in diameter is 

 1416 inches ; multiplying by the thickness, Jths of an 

 inch, we have the area of the surface of separation, 

 'J'j(j2 ; and therefore t!ie strength to resist the punch- 

 ing^ is that of a bar of iron having a sectional area of 

 'juare inches to resist fracture by tensive strain. 

 The weight required to tear asunder a bar of iron i 

 square inch in sectional area, ia found, by experiment, 

 to be about 20 tons ; and the weight to tear asunder 

 3562 square inches would, therefore, be about 61 tons, 

 which we reckon as the force required for punching the 

 hole such as we have described. 



abject of shearing strain is, upon the whole, 

 somewhat obscure. The experiments have been few, 

 and niade rather with a view to the solution of other 

 questions than the determination of a law as to this 

 strain. We would therefore caution the practical man 

 against placing too much dependence on any computa- 

 tions made in respect of it. Where ho is in doubt, aud 

 has no case practically carried out to which he may refer, 



it is far better that he should make experiments for 

 himself ; or, in the absence of data which he mi"hi 

 deduce from them, at least he should make his work 

 rather in excess of strength than otherwise. Great evils 

 may often result from the execution of work, where the 

 dimensions are too closely approximated to the results of 

 calculation as to strains and strength. These evils are of 

 an uncertain character they may occur unexpectedly 

 under circumstances that may aggravate the mischief 

 they cause ; great expense may be incurred, limbs may 

 be broken, life may be endangered or destroyed, and all 

 because material has been grudgingly employed or dis- 

 proportionally applied. But when strength is given in 

 excess, to any structure intended to be permanent, the 

 first evil, that of additional cost, is the only one i tis 

 known as to amount, is undergone, and appears not 

 again and the artificer has the satisfaction of thinking, 

 that if difficulties or dangers arise during the use of the 

 work he has contrived and formed, it must be from 

 adventitious causes for which he cannot be held blame- 

 able. 



Indeed, the whole subject of strength of materials is 

 in an unsatisfactory state. Every new experiment made, 

 every new work completed, adds somewhat to our prac- 

 tical knowledge in this department of mechanics. But 

 so long as the materials we use vary in quality, are 

 wanting in uniformity, and are subject to the changes 

 which moisture, temperature, and other circumstances 

 impose upon them, so long must we remain incapable of 

 estimating correctly their strengths for any particular 

 jurposes, and so long must we be prepared to make 

 arge allowances for all such variations, and for con- 

 tingencies which do not always readily suggest them- 

 selves. 



CHAPTER IV. 



SOURCES OP MECHANICAL POWER. 



Contents. MUSCULAR FORCE WIND, DIRECT, OBLIQUE; WINDMILLS, SAILS, GOVERNORS WATERWHEELS UNDER- 



OT, OVERSHOT, BREAST, AND COMBINED DAMS AND LEADS TURBINES HYDRAULIC RAM WEIQ HI FALLING 

 BODIES SPRINGS HYDRAULIC LIFT AND CRANE HEAT AND ELECTRICITr. 



THE principal sources of power may be classed under 

 five heads. 



1. Muscular force of men and animals. 



% Natural movements of air. 



3. Natural movement of water. 



4. Weight and elasticity of bodies. 



5. Heat, electricity, magnetism, and chemical action. 

 .. MUSCULAR POWER OF MEN AND ANIMALS. 



It is not our province to discuss the mode in which the 

 muscles of men and animals are put in action. This is a 

 question which belongs to the physiologist. Suffice it to 

 say, that the mechanism of animal structure is of that 

 most perfect kind, which characterises all the works of 

 Him who designed and executed it. The simple effort 

 of will, or whatever that particular mental faculty be 

 called, appears to communicate itself through the nerves 

 which pervade the whole animal frame like a network of 

 electric wires, and to operate immediately on the mus- 

 cular tissue. The muscles, so far as we understand their 

 nature, appear to have no innate force of their own, but 

 are merely organised instruments put in action by the 

 influence transmitted to them by the nerves, just as the 

 index of an electric telegraph is perfectly inert until it 

 is deflected, one way or other, by the subtile magnetic 

 influence transmitted to it through the electric wire. 

 Notwithstanding the immense variety of movements of 

 which the different parts of the animal frame are capable, 

 the action of the muscles, which effect those movements, 

 is of one kind only contraction in length, accompanied 

 by expansion in diameter. 



The eyes are caused to rotate in their sockets, and 

 their focus as optical instruments can be varied ; the 

 lips, the tongue, the throat, and the jaws are moved so 



VOL. i. 



as to give voice to musical notes and articulate language; 

 the shoulders, arms, wrists, hands, and fingers are put 

 in motion so as to enable man to lift heavy weights, or to 

 manipulate with consummate delicacy ; the back, body, 

 the legs and feet, are moved so that man may walk, 

 run, or leap, row, or perform feats of strength and 

 agility. And yet every one of these motions is effected 

 by the longitudinal contractions of muscles under the 

 nervous influence of volition. The frame-work of this 

 exquisite machinery is the skeleton, consisting of 

 numerous bones joined together. The form, length, 

 strength, and situation of every bone have been devised 

 with most minute care to suit its particular object. 

 Each bone plays the part of a beam, and has attached to 

 it a tendon or strong cord near its joint or fulcrum. 

 This tendon is the end or continuation of a bundle of 

 fleshy fibres, which constitute a muscle, fixed at the op- 

 posite end to some other part of the frame-work ; and 

 as these fibres contract in length under the nervous in- 

 fluence, the tendon or cord is pulled, and the bone or 

 lever caused to move round its joint or fulcrum. 



We may suppose A B (Fig. 99) to represent a fixed 

 bar, haying a joint at B fitted with a lever B C, from the 

 extremity of which a weight is suspended ; and D E a 

 cord fixed at D to the bar A B, and at E to the lever 

 B C. By shortening the cord D E we cause the lever 

 to turn about its fulcrum B, to gome such position as 

 that marked by the dotted lines E' C'. So in the human 

 arm (Fig. 100), the upper bone is the bar jointed at the 

 elbow ; the radius bone terminates in the hand, in which 

 a weight may be placed ; the cord is the biceps muscle, 

 fixed at the upper end, and terminating at the lower 

 end in a tondon, which is fixed to the radius. The 



5u 



