IN 



MECHANICAL PHILOSOPHY. STATICS. 



[HIST AND MOTION. 



whose weight u inappreciable, can bo found sufficiently 

 rigid to support the weight* I' and Q, however small, and 

 till remain perfectly straight under their pressure, an< 

 that of the sharp edge at F. It is true that anothe 

 proposition of Statin would enablo us to take into 

 account the weight of the bar A U. 



If the bar AB (Fig. 2) were uniform throughout in 

 thickness and material, the bar would balance itself on 

 the edge F, pro- v F " 

 Tided a weight 7, 

 enual the weight 

 of toe portion of r>f 

 the bar A F, Li 

 were suspended from the point 6, F & being equal the 

 Klf of A F : and a weight, }>, equal the weight of the 

 portion of the bar F B, suspended from a, F a being 

 equal the half of BF. 



Supposing the difficulty of the weight of the bar thus 

 obviated, there would still remain another difficulty in 

 the way of a perfect experimental proof of our simple 

 proposition. According to theory, the slightest addi- 

 tional weight, added to either of the weights P or Q, 

 ought to destroy the equilibrium of the bar AB, and 

 alter its perfectly horizontal position. But this supposes 

 that the edge of the support F will exercise no friction 

 on the surface of the rod A B. By a proper choice of 

 materials, for the rod and the support, and also of the 

 angle of the edge of the support, this friction may be 

 considerably diminished, but it can never bo absolutely 

 destroyed. If we could succeed in fulfilling all the con- 

 ditions we have indicated as necessary for the experi- 

 mental proof of the very simple proposition of our science, 

 which we have enunciated, we should be able to construct 

 a perfect balance. That these difficulties are real, and 

 not merely imaginary, is proved by the fact that 

 balance, sufficiently sensitive and accurate to supply the 

 wants of the modern analytical chemist, is a very expen- 

 sive instrument, and requires great skill and accuracy, as 

 well as scientific knowledge, for its construction. 



Though we cannot appeal to experiment for a rigid 

 proof of our propositions, if we make the necessary 

 allowances for the difference between the bodies on 

 which our experiments are conducted, and the imaginary 

 bodies which our science supposes perfectly rigid, and 

 so forth, careful experiments will serve not only to give 

 us clearer views of our science, but also to confirm our 

 confidence in our abstract reasonings, by the approximate 

 coincidence of our experimental results with our 

 theoretical conclusions. 



Thus, if in the experiment before alluded to, we make 

 the necessary allowance for the weight of the bar, by 

 applying the small weights p and q to the points a and 

 6, our experiments will approximate to the theoretical 

 proposition in proportion as the friction of F on the bar 

 is diminished, and the bar A B is perfectly straight and 

 accurately divided at the points a and b (Fig. 2). 



REST OR EQUILIBRIUM Having defined a ma- 

 terial particle and a rigid solid body, and their theoretical 

 properties and condition, we must next consider what 

 we mean by their rest or motion. Wo say that a body or 

 a particle is in motion when wo perceive the body or par- 

 ticle to change its position, and that it is at rest when it 

 does not change its position. This clearly implies, how- 

 ever, that we nave some means of measuring this altera- 

 tion or change of position, by reference to other bodies 

 which we conceive to bo at rest. Hence it happens that 

 what we suppose to be rest and motion, are generally 

 only apparent rest and motion, and that there is no sub- 

 ject on which our senses more frequently lead us to form 

 erroneous conclusions than when wo attempt to dis- 

 criminate the real or absolute rest and motion of objects 

 from their apparent rest or motion. When we see a body 

 change its position relatively to other bodies, we cannot 

 tell whether the body which seems to move really does 

 so or not, till we know whether the bodies relatively to 

 which it api>cars to change its position, are themselves in 

 a state of rest, or whether they aro all moving together. 

 It may so happen that the bodies may bo moving, though 

 we are ourselves unconscious of their motion ; and in this 



case the body which apparently moves may bo really at 

 rest. Instances of this kind are of daily occurrence. A 

 person on board ship, whore his own body, as well as all 

 the surrounding parts of the ship are apparently at rest, 

 sees all the objects which the ship passes, carried, as it 

 were, past him with great velocity ; and were he not con- 

 scions, from other considerations, that the ship on wlm h 

 he stands were really in motion, he would have some 

 difficulty in conceiving that the apparent motion of tins 

 stationary objects the ship passes by, was not real instead 

 of imaginary. This is strikingly illustrated by looking 

 out of a railway carriage when moving quickly ; the ob- 

 jects, such aa trees and houses, near the carriage, aro 

 apparently carried by the window with great rapidity, 

 while those at a greater distance scorn to pass more slowly. 

 If, while waiting at a station, a train pass slowly by, it is 

 often very difficult to tell whether the train in which ue 

 are seated be at rest or in motion, unless wo correct our 

 impression by looking out of the opposite window, v 

 we can compare the position of the train with the fixed 

 objects of the station. 



APPARENT REST OR MOTION OF HEAVENLY 

 BODIES. A popular knowledge of astronomy is now so 

 common, that we have no difficulty in persuading 

 sons that the apparent motion of the sun and stars in 

 the heavens is not real. Yet this is a fact which can only 

 be demonstrated by a long course of intricate reasoning, 

 founded on an immense number of careful observations. 



To an ordinary observer, the vault of heaven, studded 

 with stars, appears to revolve round an imaginary axis, 

 while the earth seems perfectly at rest ; each of the fixed 

 stars describes a circle, which brings it back to the posi- 

 tion in which it was first observed iii an invariable inter- 

 val of about 23 hours 66 minutes. What are called the 

 fixed stars seem all to move together with the vault of 

 heaven, and never to change their relative positions 

 with respect to one another. The planets and comets, as 

 well as the suu and moon, have an apparent motion 

 among the fixed stars. In the case of the planets, comets, 

 and moon, this apparent motion is exceedingly complex. 

 Sometimes a planet will appear to move forward with 

 great rapidity among the stars of a constellation ; then 

 it will come, as it were, to a stand-still, remain some timo 

 at rest, and then move backward. Ancient astronomers 

 were well acquainted with the phenomena of real and 

 apparent motion ; yet after centuries of painful research 

 and the invention of most complicated motions, to ac- 

 count for the apparent paths of the planets on the vault, 

 of heaven without avail, it was reserved for the genius 

 of Copernicus and Kepler to resolve these motions into 

 simpler ones, on the simple hypothesis that all the 

 planets move round the sun in orbits nearly elliptical, 

 and are never at rest. 



Astronomy teaches us that every object on the earth's 

 surface which appears to us at rest, ia really subject, 

 along with the earth on which it is placed, to two 

 motions ; one by which it is carried round the earth's 

 axis by its diurnal rotation, and another by which it do- 

 scribes the earth's orbit round the sun in a year. 



From these considerations it appears that there can bo 

 no absolute rest for any particle of matter by which we 

 aro surrounded ; that perpetual motion is the real con- 

 dition of all material objects ; and that when we. apply 

 he reasonings and principles of the science of statics to 

 nature, it is the apparent and not real rest of bodies to 

 which wo must have regard. 



In the application of the principles and conclusions of 



italics to nature, we may consider the earth as absolutely 



ixed and at rest, and neglect its real motion without 



ntroducing any sensible error into our experiments. 



According to the law of inertia, all the bodies on the 



arth will partake of the earth's motion, and wo know of 



no force which will deprive them of this motion ; if, 



herefore, any forces produce the relative motion or rest 



f a terrestrial body, compared with bodies fixed witli 



regard to the earth, that relative rest or motion will bo 



he same whether the earth be really at rest or in motion. 



L familiar instance may make this assertion clear. If 



a ship under the influence of steam and tide, bo moving 



