THE IEEIGATION AGE. 



945 



2/t 2h \ 2h 



= tg = , also t 2 = or / -\l , 



* 9 ^ Q 



4 



hence v = g 



2h 

 g 



These simple relations are very important as the force 

 of gravity has to be dealt with everywhere, especially in 

 hydraulic problems. 



6. Applied Problems. 



1. What is the velocity of a falling body at the end of 

 the 7th second? 



Answer : 7 X 32.16 = 225.12 ft. 



2. What is the distance the body has fallen through in 

 7 seconds ? 



t'S 7 X 7 X 3216 



Answer: h =: = = 49 X 16.08 = 



2 2 



787.92 ft. 



3. How long will it take a body to fall 50 ft? 



I Zh / 2x50 



t = \l = \l ~ - V 3.1094 = 1.763 seconds. 

 ' g * 3216 



4. What is the velocity of a body after having fallen 

 a distance of 50 ft.? 



V = V 2g/i ' = V 2 X 32.16 X 50 = V 33 - 16 = 

 56.701 ft. 



This checks the answer under 3, for if we multiply 1.763 

 by 32.16 we get 56.70 ft. 



5. Through what distance must a body fall to acquire a 

 velocity of 4 ft. per second? 



For the solution of this problem use the formula : 



_ v = V 2gh in which g = 32.16 and h = the required 

 height; square both sides of the equation: 



v* = 2gh 



Divide both sides by 2g: 



v*/2g = h 



Substitute the given quantities : 



4 X 4 -r- 2 X 32.16; for ordinary problems it is near 

 enough to use 32 instead of 32.16; hence: 



h = 16 -4- 64 = J4 = 3 inches. 



This shows that after a body has fallen 3 inches it 

 has acquired a velocity of 4 ft per second. 



Summary of Formulas is herewith given, referring to 

 them in future by the letter given. 



Let in all the formulae the following terms be used : 



g = acceleration of gravity = 32.16 ft. per sec. 

 t = no. of seconds. 



v = velocity in ft. per second. 



h = height of fall in ft. ; also termed the head when flow- 

 ing water is considered, then 



Formula^ : v = tg 



B : h = t'g/Z 



C : v = \/Zgh 

 D ih if -r- Zg 



These formulae establish the relation between velocity, 

 time and height of fall. 



Article VIII. The Three States of Matter. 



1. General Principles. 



All things in Nature are either solids, fluids or vapors 

 (gases), and some substances, like water, are known in all 

 three states, namely in the solid form as ice and snow, as 

 a fluid under normal conditions, and in the form of steam 

 when heated to a certain point. 



The state of a solid can then be denned that in a solid 

 the molecules lie very near to each other so that is requires 

 force to separate them ; this proves the existence of an 

 attractive force between the molecules, tending to pull the 

 particles together ; this force is called cohesion. It is as- 

 sumed that there is also a repellant force active between 

 the molecules tending to separate them ; this force is called 

 repulsion. Under the influence of these two forces the 

 molecules are in a constant state of vibration ; when a con- 

 traction of a substance takes place, due either to pressure 

 or cold, then the cohesion increases, pulling the particles 

 together; if heat is applied to a body the repulsion is in- 

 creased and causes the expansion of the body. This ex- 

 pansion may become so great that the repulsion balances 



the cohesion and then the state of solid is changed to that 

 .of a fluid; in this state the body offers little resistance to 

 the separation of its particles. If heat is continued to be 

 applied the repulsion grows and overbalances the cohesion; 

 then the state of the fluid changes to that of a gas, in which 

 state the molecules tend to separate indefinitely and force 

 must be applied to keep them together; thus, if sulphurated 

 hydrogen is, for instance, set free by letting sulphuric acid 

 act on iron sulphide, the gas will permeate at once the 

 whole room, which is proved that it can be smelled all over 

 the room. 



Generally speaking, all substances can be transformed 

 into the three states of matter by the agencies of heat or 

 pressure, or both. Thus gold may be melted and even vapor- 

 ized by using sufficiently high temperature; also oxygen 

 gas may be made fluid by applying high pressure and cold, 

 and may even be made solid by applying intense cold and 

 very high pressure. The terms solids, fluids and gases apply 

 to bodies that under ordinary conditions are solid, fluid or 

 gaseous. 



2. Special Properties of Solids. 



a. Hardness. All solids offer a certain resistance to 

 being broken. The Mohr's Scale of Hardness is used to desig- 

 nate the different degrees of hardness, namely: (1) .Talc, 

 (2) Selemite, (3) Calcite, (4) Fluorite, (5) Apatite, (6) 

 Adularia, (7) Quartz, (8) Topaz, (9) Sapphire, and (10) 

 Diamond. To test any substance for its hardness try to 

 scratch with it the above named substances in succession; 

 if it scratches, for instance, calcite but does not scratch 

 fluorite its hardness is between 3 and 4 of Mohr"s Scale. 



b. Malleability is the property of being widened out 

 under the hammer, like lead or gold. 



Ductility is the property of some substances to be drawn 

 out in wires. The most ductile substance is platinum, which 

 has been drawn into wires so fine that its diameter equals 

 .00003 inch. 



c. Tenacity is called the resistance different substances 

 offer to being broken or ruptured. It is measured by the 

 tensile strength of structural or building materials. 



d. Elasticity is the tendency of bodies to assume their 

 original form after having undergone a distortion ; this prop- 

 erty is also called rigidity when the body offers resistance 

 only to distortion. 



Forces which tend to produce alterations or distortions 

 in bodies are called stresses ; they are shearing, twisting and 

 bending stresses. The bending stresses may be either cotn- 

 pressive or tensile according to whether the forces tend to 

 compress or elongate the fibres of the body under stress. 



3. Properties of Fluids. 



a. The surface of fluids at rest is horizontal. There 

 being no rigidity between the molecules of a fluid their shape 

 is altered by the least force so that when a fluid is at rest 

 its surface is horizontal and it fills the form of the con- 

 taining vessel. That the surface of a liquid must be at right 

 angles to the force of gravity is seen 

 from the following deduction; referring 

 to Fig. 64, let EC be the surface of a 

 fluid not at rest and let A be a particle 

 of the fluid; the force of gravity AG 

 pulls on A in a vertical direction and 

 AG may be decomposed into Ad, acting 

 normally to the surface of the fluid, and 

 AGi\, acting in a horizontal direction; 

 the force AGi is neutralized by the body 

 of the fluid but the force AGa. will pull 

 point A down toward C and this will 

 be kept up with all particles until the 

 surface BC is normal to AG, or with 

 other words until the surface of the fluid is level. 



b. The pressure in fluids 

 is transmitted equally in all di- 

 rections. 



Fluids transmit pressure 

 equally in all directions. An 

 application of this principle is 

 shown in Fig. 65, which repre- 

 sents a hydrostatic press, con- 

 sisting of 2 cylinders c and 

 C in which pistons p and P 

 can move up and down; a 

 valve Vi admits water to cylin- 

 der c and valve v admits water to cylinder C so that if piston 



Fig. 64 



Fig. 65 



