\TEICHT.] 



MECHANICAL PHILOSOPHY STATICS. 



691 



rapidly through smooth water, all mechanical powers, 

 such as blocks and pulleys, the windlass, and all the 

 parts of the most complicated steam-engine will act 

 under precisely the same circumstances, exert the same 

 forces, be brought to a state of apparent rest or motion 

 compared with the ship as a fixed object, whether the 

 ship be at rest or in motion. A game of billiards, which 

 requires considerable practical skill in mechanical science, 

 may be played in the cabin of a ship without the players 

 being aware whether the ship is at rest or in motion. 

 Though, with respect to the earth, the balls, which were 

 apparently at rest while the ship was moving, would be 

 iu reality not at rest, but moving with the ship. 



MEASURE OF FORCE DYNAMOMETERS. 

 We regard all forces as equal which produce the same 

 mechanical effects ; and in statics we consider forces as 

 equal, which produce the same effects, when applied in a 

 similar manner, in bringing a body into a state of equi- 

 librium. Instruments, by means of which these effects are 

 estimated, are called dynamometers, or force measurers. 



A very simple dynamometer consists of a thin flat bar 

 of steel, ABC, bent into an angle at B, and properly 

 tempered, so that if any force be applied at A and C, to 

 bring the extre- 

 mities nearer to- 

 gether, the force 

 of elasticity of 

 the steel will 

 cause the extre- 

 mities, A and C, 

 to resume their 



ion as soon as the forces are removed. The greater 

 the forces applied to A and C, the nearer these extre- 

 mities of the bar will be brought to one another. 

 To measure this effect, a circular arc of metal, 

 A C 1), is fixed perpendicularly to the surface of the 

 steel bar at A, passing freely through an opening in the 

 other extremity of the bar at C. Another arc, C A E, 

 is similarly fixed at C, passing through an opening at A. 

 Riugs are fixed at 1) and K for the convenient application 

 of forces whose effects are to be estimated ; and one of the 

 arcs, A D, is graduated by a number of equal divisions. 



If the extremity K (Fig- 4) of the dynamometer be 



Fig. 3. 



Fig. i. 



fixed to a beam, and a weight, P, 

 hung from the ring at D, the gradu- 

 ated arc will show the statical effects 

 of the weight P in bringing the dyna- 

 mometer to a state of rest, with the 

 extremities of the bent bar nearer to 

 each other than they were before the 

 application of the weight P. If, 

 instead of applying a weight P, wo 

 pull with our hand a string at- 

 tached to D (Fig. 5), till we bring 

 the graduated part of the arc at A to 

 the same division to which the weight 

 P brought it, we produce with our 

 hand a similar statical effect to that 

 produced by the weight. We there- 

 fore conclude that the forces exerted 

 by the weight and by the hand are 

 equal to one another, though they are evidently forces 

 of a very different character, the 

 force of the weight being produced 

 by the earth's attraction for the 

 particles of matter of which it is 

 composed, and the force exerted 

 by the arm being derived from the 

 contractions of the muscular fibres 

 of the muscles of the arm, duo to 

 gome force which we call the mus- B 

 cvilar force, of the nature of which 

 we are perfectly ignorant. 



There are many other dynamo- 

 meters besides that just described, 

 guoh as one in which the statical 

 effects of a force causing a spiral 

 pring of wire contained in a metal 

 cylinder to be compressed, is mea- 



sured on a graduated rod, as in the accompanying figure 

 (Fig. 6). The various kinds of balances and steel 

 yards, which will be described hereafter, are all 

 dynamometers. 



UNIT OF FORCE. The experiment on the 

 dynamometer, just described, would lead us to 

 infer, what is found to be true in practice, that 

 weight is the most convenient measure of force 

 which we can adopt in statics. We say that a 

 force of ten or twelve pounds is exerted on a 

 body, if the force produce the same statical 

 effect on the body which a weight of ten or 

 twelve pounds applied ill a similar way would 

 produce. The unit of force generally adopted in 

 this country is that called a pound weight. But 

 here we may be met with the inquiry, what is a 

 pound weight ? This is a very important ques- 

 tion, and has been determined by legislative 

 enactment, after careful deliberation, and the 

 report of a scientific commission appointed for 

 the consideration of the difficult subject of 

 standard weights and measures. 



POUNDS TROY AND AVOIRDUPOIS. 

 By the Act of Parliament (5th George IV., c. 74, passed 

 in the year 1824, sections 4 and 5), it is enacted " That 

 from and after the first day of May, 1825, the standard 

 brass weight of one pound troy weight, made in the year 

 of 1758, now in the custody of the clerk of the House of 

 Commons, shall be, and the same is hereby declared to be, 

 the original and genuine standard of measure of weight, 

 and that such brass weight shall be, and is hereby de- 

 clared to be, the original and genuine standard measure 

 of weight, and that such brass weight shall be and is 

 hereby denominated the Imperial Standard Troy Pound, 

 and shall be, and is hereby declared to bo, the unit or 

 only standard measure of weight from which all other 

 weights shall be derived, computed, and ascertained, and 

 that one twelfth part of the said troy pound shall be an 

 ounce, and that one twentieth part of such ounce shall be 

 a pennyweight, and that one twenty-fourth part of such 

 pennyweight shall be a grain ; so that 5,760 such grains 

 shall be a troy pound, and that 7,000 such grains shall be, 

 and they are hereby declared to be, a pound avoirdupois, 

 and that one sixteenth part of the said pound avoirdupois 

 shall be an ounce avoirdupois, and that one sixteenth 

 part of such ounce shall bo a dram. 



"And whereas it is expedient that the said standard 

 troy pound, if lost, destroyed, defaced, or otherwise 

 injured, should be restored of the same weight by re- 

 ference to some invariable natural standard ; and whereas 

 it has been ascertained by the commissioners appointed 

 by his Majesty to inquire into the subject of weights and 

 measures, that a cubic inch of distilled water, weighed in 

 air by brass weights at the temperature of 62 degrees of 

 Fahrenheit's thermometer, the barometer being at 30 

 inches, is equal to 252 grains, and 456 thousandth parts 

 of a grain, of which, as aforesaid, the Imperial Standard 

 Troy Pound contains 5760 : Be it therefore enacted, 

 that if at any time hereafter the said Imperial Troy 

 Pound shall be lost, or shall in any manner be destroyed, 

 defaced, or otherwise injured, it shall and may be re- 

 stored by making, under the direction of the Lord High 

 Treasurer, or the Commissioners of His Majesty's 

 Treasury of the United Kingdom of Great Britain and 

 Ireland, or any three of them for the time being, a new 

 standard troy pound, bearing the same proportion to the 

 weight of a cubic inch of distilled water, as the said 

 standard pound, hereby established, bears to such cubic 

 inch of water." 



From this Act of Parliament it appears that the troy 

 pound is a certain arbitrary piece of brass, which, weighed 

 in air at a temperature of 62 Fahrenheit, the mercury 

 in the barometer standing at a height of 30 inches, is 

 equal to the weight of 22 cubic inches, and 815 thousand 

 parts of a cubic inch of distilled water. Distilled water 

 is therefore the natural standard to which the unit of 

 weight is ultimately referred. This standard, however, 

 is referred to a cubic inch, or a volume of water an inch 

 in height, an inch in breadth, and an inch in depth. 



