APPLIED MECHANICS. 



[DEHJJITIOW or POWER. 



' to them in certain directions, it is not 

 ditlicult u> form general rules by which tlia trength of 



r beauts dilii MH_- in dimei. -heir strength to 



resist strains in certain <>t)i<T dir. v be cora- 



l-ut.-d. The careful mechanical designer either makes 



rmients for himself, or accepts the observations of 

 other*, and devises his structures in such a manner as to 

 take advantage of these results. Practice in dt-sign, ami 



.out olisei .iiocessful works, do much to 



form tin' oyo of a designer, so that tho mere appearance 

 of a thing, whether drawn or executed, satisfies his sense 

 of jti>t proportion, or the reverse. It is indeed a wonder- 

 ful, as it is a most valuable property of the mind, that 

 it can readily recognise and prefer the useful and suit- 

 able ; and, as the just and the true recommend them- 

 selves to the mental and moral sense, so does the fitting 

 in design recommend itself to the eye. Some individuals 

 are gifted by nature with a keener sense and readier 

 power of discriminating these qualities, and can there- 

 fore criticise more truly, or design more skilfully than 

 others. But where there is a love for mechanical pur- 

 suits, or a desire to study mechanical works, we believe 

 much of this power may be readily acquired. 



POWER. In the dynamical branch of Mechanics 

 there are subjects of great interest and extensive appli- 

 cation which demand the utmost attention ; we allude 

 to the means of deriving and communicating power. 

 If we ask ourselves what power means, we can scarcely 

 define it by any simple term ; we may say that it is the 

 capability of doing work or producing change. We start 

 with the idea, which is a true one, that all matter is 

 inert, incapable of receiving motion, of being brought to 

 rest, or of undergoing any kind of change whatever of 

 its own accord ; some extraneous force or power has to 

 be impressed upon it, and the quantity of change effected 

 is the work done. When we lift a weight from the 

 ground, the hand exerts a certain amount of power, and 



Fig. 3. 



provinces a certain amount of work ; an act of mental 

 Tolition communicates through the nerves, in some way 

 unknown to us, an influence to the muscles of our arm, 

 which causes them to contract. The muscles are attached 

 at both ends to the bones, which are rigid levers jointed 

 together. One end of sqch a bone or lever being fixed, 

 as at the elbow-joint, and the muscle being contracted, 

 the other end of the lever, to which is attached the hand 

 holding the weight, is caused to move through a cer- 

 tain space, and thus to lift the weight a certain height 



'-') 

 This is a case of power employed in producing motion ; 



but, after the weight is lifted, power must still be exer- 

 cised in retaining it in its position, for were the nnic-l.-s 

 no mutant relaxed, the hand and weight would drop 

 downwards. If such be the case, we may at first sight 

 imagine that our notion respecting the inertness of mat- 

 ter is incorrect, otherwise the hand and weight would of 

 themselves remain where our muscular power had placed 

 them. But, looking a little more closely into the facts, 

 we find that while the matter with which we deal is 

 really inert, there is a constant power acting upon it in 

 Jtion to our muscular power the power of gravi- 

 tating attraction, by which all bodies near the earth's 

 surface are drawn down to it. 



This power ha* been found ..ntand 



oWrvation, to act equally on all bodies and all parts of 



' every body ; and the measure of the force with which it 

 acts on any body is the weight of that Ixnly. li 

 mating power, UMrefore, wri^ht is tin- measure of one 

 important element ; and if we know t which 



any given power can lift from the earth, we have correct 

 data for calculating its amount : in fact, w<> know the 

 quantity of matter on which the power has effected a 

 change. But there is another element of power quite aa 

 important as the quantity of matter acted on. we mean 

 the quantity of change produced upon it. If we find a 

 certain amount of exertion necessary to lift a weight one 

 foot from the ground, wo shall find greater exertion 

 necessary to lift it two feet. The change in both cases 

 effected by the power applied, is a change of posit 

 but the amount of change that is, the distance tin 

 which the weight is moved is in the one case double 

 that in the other. Experiment and observation, as well 

 as reasoning, prove distinctly, that the force required to 

 lift a given weight, is exactly proportional to the dis- 

 tance through which it is lifted. \Ve thni acquire the 

 means of computing another element of power ; and can 

 combine this element, expressive of the amount of 

 change effected, with the former, which expresses the 

 quantity of matter upon which the change is produced. 



In comparing numerically one power with another, 

 we are therefore warranted in multiplying the ( 

 lifted in each case, by the distance through which it is 

 lifted, and comparing the results. Thus, if one man lift 

 201bs. 1 foot high, and another lift 301bs 1 foot high, 

 we say that the powers exerted by the two men are aa 

 20 to 30, or as 2 to 3 ; or if one lift 20 Ibs. 2 feet high, 

 and the other lift 20 Ibs. 3 feet high, the powers they 

 exert are ae 20 multiplied by 2 (that is, 40), to 20 mul- 

 tiplied by 3 (that is, 60) ; or as 2 to 3. Asrain, let the 

 one lift 20 Ibs. 2 feet high, and the other 90 Ibs. 3 feet 

 high, their powers are as 20 multiplied by 2 (that is, 40), 

 to 30 multiplied by 3 (that is, 90) ; or, more simply, as 

 4 to 9. 



But, recurring to our definition of power 

 as being the capability of effecting change, 

 we must see that there is yet another ele- 

 ment of calculation necessary for estimat- 

 ing different capabilities ; as yet we have 

 reckoned only the amount of work done, 

 and have paid no regard to tho time re- 

 quired for doing it. A few coral bisects, 

 labouring continuously for centuries, may 

 form an island, which it would require 

 thousands of workmen to raise in a short 

 period ; but yet the power of each work- 

 man far exceeds that of the insect, and the 

 two powers can only be compared by sup- 

 posing them to be exerted during equal times. Now, 

 it is clear that a certain work being done, the shorter 

 the period required for doing it, the greater is tho 

 power exerted ; and conversely. In comparing powers 

 numerically, we must therefore divide th work done 

 by the time occupied in performing it. Suppose one 

 man lifts 20 Ibs. 12 feet high in 3 niintiies, and 

 'mr lifts 30 Ibs. 10 feet high in 2 minutes, the 

 work done by each is 20 Ibs. X 12 feet, or 1MO, and 

 30 Ibs. X 10 feet, or 300, respectively ; but 240 divided 

 by 3 minutes give 80, and 300 divided by 2 minutes 

 give 150 : the powers of the two are therefore in the pro- 

 portion of these numbers, 80 to 150 ; or, more simply, 

 8 to 15. 



STANDARD OF POWER. Wo have now found 

 means of measuring all the elements of power, and so 

 determining its amount. For the sake of convenience, 

 we fix upon some standard power with which w. 

 compare others, just as we fix on a standard weight, 

 such as a pound, or a standard length, as a foot; and 

 knowing the value of several powers as compared with 

 this standard, we can estimate their values as compared 

 with one another. The standard power usually adoi 

 in practical mechanics is a horse-power, which ha* 

 defined to lie :',:;. (HKl ll.s. lifted 1 foot high in 1 minute. 

 The weight lifted, 33,000 Ibs., was determined from the 

 average of numerous experiments made with homes at 



