![gas delivery tube[15]
passes whose end is immersed under
water, it will be observed that on heating, a gas is formed
which bubbles through the water. This gas can be easily
collected, as will presently be described, and it will be found
to essentially differ from air in many respects; for instance, a
burning taper is extinguished in it as if it had been plunged
into water. If weighing had not proved to us that some
substance had been separated, the formation of the gas might
easily have escaped our notice, for it is colourless and
transparent like air, and is therefore evolved without any
striking feature. The carbonic anhydride evolved may be
weighed,[16]
and it will be seen that the sum of the weights of
the black copper oxide and carbonic anhydride is equal to the
weight of the copper carbonate[17]
originally taken, and thus
by carefully following out the various stages of all chemical
reactions we arrive at a confirmation of the law of the
indestructibility of matter.
3. Red mercury oxide (which is formed as mercury rust by
heating mercury in air) is decomposed like copper carbonate
(only by heating more slowly and at a somewhat higher
temperature), with the formation of the peculiar gas, oxygen.
For this purpose the mercury oxide is placed in a glass tube or
retort,[18]
to which a gas delivery tube is attached by means of
a cork. This tube is bent downwards, as shown in the drawing
(Fig. 1). The open end of the gas delivery tube is immersed in
a vessel filled with water, called a pneumatic trough.[19]
When
the gas begins to be evolved in the retort it is obliged, having
no other outlet, to escape through the gas delivery tube into
the water in the pneumatic trough, and therefore its evolution
will be rendered visible by the bubbles coming from this tube.
In heating the retort containing the mercury oxide, the air](https://image.slidesharecdn.com/50857-250312163850-a323c680/85/Mechanical-Vibration-Analysis-Uncertainties-and-Control-Third-Edition-Benaroya-27-320.jpg)
![contained in the apparatus is first partly expelled, owing to its
expansion by heat, and then the peculiar gas called ‘oxygen’ is
evolved, and may be easily collected as it comes off. For this
purpose a vessel (an ordinary cylinder, as in the drawing) is
filled quite full with water and its mouth closed; it is then
inverted and placed in this position under the water in the
trough; the mouth is then opened. The cylinder will remain
full of water—that is, the water will remain at a higher level in
it than in the surrounding vessel, owing to the atmospheric
pressure. The atmosphere presses on the surface of the water
in the trough, and prevents the water from flowing out of the
cylinder. The mouth of the cylinder is placed over the end of
the gas delivery tube,[20]
and the bubbles issuing from it will
rise into the cylinder and displace the water contained in it.
Gases are generally collected in this manner. When a sufficient
quantity of gas has accumulated in the cylinder it can be
clearly shown that it is not air, but another gas which is
distinguished by its capacity for vigorously supporting
combustion. In order to show this, the cylinder is closed,
under water, and removed from the bath; its mouth is then
turned upwards, and a smouldering taper plunged into it. As
is well known, a smouldering taper will be extinguished in air,
but in the gas which is given off from red mercury oxide it
burns clearly and vigorously, showing the property possessed
by this gas for supporting combustion more energetically than
air, and thus enabling it to be distinguished from the latter. It
may be observed in this experiment that, besides the
formation of oxygen, metallic mercury is formed, which,
volatilising at the high temperature required for the reaction,
condenses on the cooler parts of the retort as a mirror or in
globules. Thus two substances, mercury and oxygen, are
obtained by heating red mercury oxide. In this reaction, from](https://image.slidesharecdn.com/50857-250312163850-a323c680/85/Mechanical-Vibration-Analysis-Uncertainties-and-Control-Third-Edition-Benaroya-28-320.jpg)
![by their mutual chemical action, two new substances, one
insoluble in water, and the other remaining in solution. Here,
from two substances, two others are obtained, consequently
there occurred a reaction of substitution. The water served
only to convert the re-acting substances into a liquid and
mobile state. If the lunar caustic and salt be dried[21]
and
weighed, and if about 58½ grams[22]
of salt and 170 grams of
lunar caustic be taken, then 143½ grams of insoluble silver
chloride and 85 grams of sodium nitrate will be obtained. The
sum of the weights of the re-acting and resultant substances
are seen to be similar and equal to 228½ grams, which
necessarily follows from the law of the indestructibility of
matter.
Accepting the truth of the above law, the question naturally
arises as to whether there is any limit to the various chemical
transformations, or are they unrestricted in number—that is to
say, is it possible from a given substance to obtain an
equivalent quantity of any other substance? In other words,
does there exist a perpetual and infinite change of one kind of
material into every other kind, or is the cycle of these
transformations limited? This is the second essential problem
of Chemistry, a question of quality of matter, and one, it is
evident, which is more complicated than the question of
quantity. It cannot be solved by a mere superficial glance at
the subject. Indeed, on seeing how all the varied forms and
colours of plants are built up from air and the elements of the
soil, and how metallic iron can be transformed into colours
such as inks and Prussian blue, we might be led to think that
there is no end to the qualitative changes to which matter is
susceptible. But, on the other hand, the experiences of
everyday life compel us to acknowledge that food cannot be
made out of a stone, or gold out of copper. Thus a definite](https://image.slidesharecdn.com/50857-250312163850-a323c680/85/Mechanical-Vibration-Analysis-Uncertainties-and-Control-Third-Edition-Benaroya-30-320.jpg)
![Thus they saw that from a metallic substance which is
unfitted for use they could obtain another metallic substance
which is ductile and valuable for many technical purposes.
Furthermore, they took this lead and obtained silver, a still
more valuable metal, from it. Thus they might easily conclude
that it was possible to ennoble metals by means of a whole
series of transmutations—that is to say, to obtain from them
those which are more and more precious. Having got silver
from lead, they assumed that it would be possible to obtain
gold from silver. The mistake they made was that they never
weighed or measured the substances used or produced in
their experiments. Had they done so, they would have learnt
that the weight of the lead was much less than that of the
galena from which it was obtained, and the weight of the
silver infinitesimal compared with that of the lead. Had they
looked more closely into the process of the extraction of the
silver from lead (and silver at the present time is chiefly
obtained from the lead ores) they would have seen that the
lead does not change into silver, but that it only contains a
certain small quantity of it, and this amount having once been
separated from the lead it cannot by any further operation
give more. The silver which the alchemists extracted from the
lead was in the lead, and was not obtained by a chemical
change of the lead itself. This is now well known from
experiment, but the first view of the nature of the process
was very likely to be an erroneous one.[23]
The methods of
research adopted by the alchemists could give but little
success, for they did not set themselves clear and simple
questions whose answers would aid them to make further
progress. Thus though they did not arrive at any exact law,
they left nevertheless numerous and useful experimental data
as an inheritance to chemistry; they investigated, in particular,](https://image.slidesharecdn.com/50857-250312163850-a323c680/85/Mechanical-Vibration-Analysis-Uncertainties-and-Control-Third-Edition-Benaroya-32-320.jpg)
![consumed or enters into combination. Carbon reduces earthy
substances because it is rich in phlogiston, and gives up a
portion of its phlogiston to the substance reduced. Thus Stahl
supposed metals to be compound substances consisting of
phlogiston and an earthy substance or oxide. This hypothesis
is distinguished for its very great simplicity, and for this and
other reasons it acquired many supporters.[24]
Fig. 3.—Lavoisier's apparatus for determining
the composition of air and the reason of
metals increasing in weight when they are
calcined in air.
Lavoisier proved by means of the balance that every case of
rusting of metals or oxidation, or of combustion, is
accompanied by an increase in weight at the expense of the
atmosphere. He formed, therefore, the natural opinion that
the heavier substance is more complex than the lighter one.
[25]
Lavoisier's celebrated experiment, made in 1774, gave
indubitable support to his opinion, which in many respects
was contradictory to Stahl's doctrine. Lavoisier poured four](https://image.slidesharecdn.com/50857-250312163850-a323c680/85/Mechanical-Vibration-Analysis-Uncertainties-and-Control-Third-Edition-Benaroya-34-320.jpg)
![made in this direction, no fact has been discovered which
could in any way support the idea of the complexity of such
well-known elements[26]
as oxygen, iron, sulphur, &c.
Therefore, from its very conception, an element is not
susceptible to reactions of decomposition.[27]
The quantity, therefore, of each element remains constant
in all chemical changes: a fact which may be deduced as a
consequence of the law of the indestructibility of matter, and
of the conception of elements themselves. Thus the equation
expressing the law of the indestructibility of matter acquires a
new and still more important signification. If we know the
quantities of the elements which occur in the re-acting
substances, and if from these substances there proceed, by
means of chemical changes, a series of new compound
substances, then the latter will together contain the same
quantity of each of the elements as there originally existed in
the re-acting substances. The essence of chemical change is
embraced in the study of how, and with what substances,
each element is combined before and after change.
In order to be able to express various chemical changes by
equations, it has been agreed to represent each element by
the first or some two letters of its (Latin) name. Thus, for
example, oxygen is represented by the letter O; nitrogen by
N; mercury (hydrargyrum) by Hg; iron (ferrum) by Fe; and so
on for all the elements, as is seen in the tables on page 24. A
compound substance is represented by placing the symbols
representing the elements of which it is made up side by side.
For example, red mercury oxide is represented by HgO, which
shows that it is composed of oxygen and mercury. Besides
this, the symbol of every element corresponds with a certain
relative quantity of it by weight, called its ‘combining’ weight,](https://image.slidesharecdn.com/50857-250312163850-a323c680/85/Mechanical-Vibration-Analysis-Uncertainties-and-Control-Third-Edition-Benaroya-38-320.jpg)
![Besides these 66 elements there have been discovered:—
Erbium, Terbium, Samarium, Thullium, Holmium, Mosandrium,
Phillipium, and several others. But their properties and
combinations, owing to their extreme rarity, are very little
known, and even their existence as independent
substances[28]
is doubtful.
It has been incontestably proved from observations on the
spectra of the heavenly bodies that many of the commoner
elements (such as H, Na, Mg, Fe) occur on the far distant
stars. This fact confirms the belief that those forms of matter
which appear on the earth as elements are widely distributed
over the entire universe. But we do not yet know why, in
nature, the mass of some elements should be greater than
that of others.[28 bis]
The capacity of each element to combine with one or
another element, and to form compounds with them which
are in a greater or less degree prone to give new and yet
more complex substances, forms the fundamental character
of each element. Thus sulphur easily combines with the
metals, oxygen, chlorine, or carbon, whilst gold and silver
enter into combinations with difficulty, and form unstable
compounds, which are easily decomposed by heat. The cause
or force which induces the elements to enter into chemical
change must be considered, as also the cause which holds
different substances in combination—that is, which endues
the substances formed with their particular degree of stability.
This cause or force is called affinity (affinitas, affinité,
Verwandtschaft), or chemical affinity.[29]
Since this force must
be regarded as exclusively an attractive force, like gravity,
many writers (for instance, Bergmann at the end of the last,
and Berthollet at the beginning of this, century) supposed](https://image.slidesharecdn.com/50857-250312163850-a323c680/85/Mechanical-Vibration-Analysis-Uncertainties-and-Control-Third-Edition-Benaroya-46-320.jpg)
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- 8. MECHANICAL ENGINEERING A Series of Textbooks and Reference Books Founding Editor L. L. Faulkner Columbus Division, Battelle Memorial Institute and Department of Mechanical Engineering The Ohio State University Columbus, Ohio 1. Spring Designer’s Handbook, Harold Carlson 2. Computer-Aided Graphics and Design, Daniel L. Ryan 3. Lubrication Fundamentals, J. George Wills 4. Solar Engineering for Domestic Buildings, William A. Himmelman 5. Applied Engineering Mechanics: Statics and Dynamics, G. Boothroyd and C. Poli 6. Centrifugal Pump Clinic, Igor J. Karassik 7. Computer-Aided Kinetics for Machine Design, Daniel L. Ryan 8. Plastics Products Design Handbook, Part A: Materials and Components; Part B: Processes and Design for Processes, edited by Edward Miller 9. Turbomachinery: Basic Theory and Applications, Earl Logan, Jr. 10. Vibrations of Shells and Plates, Werner Soedel 11. Flat and Corrugated Diaphragm Design Handbook, Mario Di Giovanni 12. Practical Stress Analysis in Engineering Design, Alexander Blake 13. An Introduction to the Design and Behavior of Bolted Joints, John H. Bickford 14. Optimal Engineering Design: Principles and Applications, James N. Siddall 15. Spring Manufacturing Handbook, Harold Carlson 16. Industrial Noise Control: Fundamentals and Applications, edited by Lewis H. Bell 17. Gears and Their Vibration: A Basic Approach to Understanding Gear Noise, J. Derek Smith 18. Chains for Power Transmission and Material Handling: Design and Applications Handbook, American Chain Association 19. Corrosion and Corrosion Protection Handbook, edited by Philip A. Schweitzer 20. Gear Drive Systems: Design and Application, Peter Lynwander 21. Controlling In-Plant Airborne Contaminants: Systems Design and Calculations, John D. Constance 22. CAD/CAM Systems Planning and Implementation, Charles S. Knox 23. Probabilistic Engineering Design: Principles and Applications, James N. Siddall 24. Traction Drives: Selection and Application, Frederick W. Heilich III and Eugene E. Shube
- 9. 25. Finite Element Methods: An Introduction, Ronald L. Huston and Chris E. Passerello 26. Mechanical Fastening of Plastics: An Engineering Handbook, Brayton Lincoln, Kenneth J. Gomes, and James F. Braden 27. Lubrication in Practice: Second Edition, edited by W. S. Robertson 28. Principles of Automated Drafting, Daniel L. Ryan 29. Practical Seal Design, edited by Leonard J. Martini 30. Engineering Documentation for CAD/CAM Applications, Charles S. Knox 31. Design Dimensioning with Computer Graphics Applications, Jerome C. Lange 32. Mechanism Analysis: Simplified Graphical and Analytical Techniques, Lyndon O. Barton 33. CAD/CAM Systems: Justification, Implementation, Productivity Measure- ment, Edward J. Preston, George W. Crawford, and Mark E. Coticchia 34. Steam Plant Calculations Manual, V. Ganapathy 35. Design Assurance for Engineers and Managers, John A. Burgess 36. Heat Transfer Fluids and Systems for Process and Energy Applications, Jasbir Singh 37. Potential Flows: Computer Graphic Solutions, Robert H. Kirchhoff 38. Computer-Aided Graphics and Design: Second Edition, Daniel L. Ryan 39. Electronically Controlled Proportional Valves: Selection and Application, Michael J. Tonyan, edited by Tobi Goldoftas 40. Pressure Gauge Handbook, AMETEK, U.S. Gauge Division, edited by Philip W. Harland 41. Fabric Filtration for Combustion Sources: Fundamentals and Basic Tech- nology, R. P. Donovan 42. Design of Mechanical Joints, Alexander Blake 43. CAD/CAM Dictionary, Edward J. Preston, George W. Crawford, and Mark E. Coticchia 44. Machinery Adhesives for Locking, Retaining, and Sealing, Girard S. Haviland 45. Couplings and Joints: Design, Selection, and Application, Jon R. Mancuso 46. Shaft Alignment Handbook, John Piotrowski 47. BASIC Programs for Steam Plant Engineers: Boilers, Combustion, Fluid Flow, and Heat Transfer, V. Ganapathy 48. Solving Mechanical Design Problems with Computer Graphics, Jerome C. Lange 49. Plastics Gearing: Selection and Application, Clifford E. Adams 50. Clutches and Brakes: Design and Selection, William C. Orthwein 51. Transducers in Mechanical and Electronic Design, Harry L. Trietley 52. Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena, edited by Lawrence E. Murr, Karl P. Staudhammer, and Marc A. Meyers 53. Magnesium Products Design, Robert S. Busk 54. How to Integrate CAD/CAM Systems: Management and Technology, William D. Engelke 55. Cam Design and Manufacture: Second Edition; with cam design software for the IBM PC and compatibles, disk included, Preben W. Jensen
- 10. 56. Solid-State AC Motor Controls: Selection and Application, Sylvester Campbell 57. Fundamentals of Robotics, David D. Ardayfio 58. Belt Selection and Application for Engineers, edited by Wallace D. Erickson 59. Developing Three-Dimensional CAD Software with the IBM PC, C. Stan Wei 60. Organizing Data for CIM Applications, Charles S. Knox, with contributions by Thomas C. Boos, Ross S. Culverhouse, and Paul F. Muchnicki 61. Computer-Aided Simulation in Railway Dynamics, by Rao V. Dukkipati and Joseph R. Amyot 62. Fiber-Reinforced Composites: Materials, Manufacturing, and Design, P. K. Mallick 63. Photoelectric Sensors and Controls: Selection and Application, Scott M. Juds 64. Finite Element Analysis with Personal Computers, Edward R. Champion, Jr. and J. Michael Ensminger 65. Ultrasonics: Fundamentals, Technology, Applications: Second Edition, Revised and Expanded, Dale Ensminger 66. Applied Finite Element Modeling: Practical Problem Solving for Engineers, Jeffrey M. Steele 67. Measurement and Instrumentation in Engineering: Principles and Basic Laboratory Experiments, Francis S. Tse and Ivan E. Morse 68. Centrifugal Pump Clinic: Second Edition, Revised and Expanded, Igor J. Karassik 69. Practical Stress Analysis in Engineering Design: Second Edition, Revised and Expanded, Alexander Blake 70. An Introduction to the Design and Behavior of Bolted Joints: Second Edition, Revised and Expanded, John H. Bickford 71. High Vacuum Technology: A Practical Guide, Marsbed H. Hablanian 72. Pressure Sensors: Selection and Application, Duane Tandeske 73. Zinc Handbook: Properties, Processing, and Use in Design, Frank Porter 74. Thermal Fatigue of Metals, Andrzej Weronski and Tadeusz Hejwowski 75. Classical and Modern Mechanisms for Engineers and Inventors, Preben W. Jensen 76. Handbook of Electronic Package Design, edited by Michael Pecht 77. Shock-Wave and High-Strain-Rate Phenomena in Materials, edited by Marc A. Meyers, Lawrence E. Murr, and Karl P. Staudhammer 78. Industrial Refrigeration: Principles, Design and Applications, P. C. Koelet 79. Applied Combustion, Eugene L. Keating 80. Engine Oils and Automotive Lubrication, edited by Wilfried J. Bartz 81. Mechanism Analysis: Simplified and Graphical Techniques, Second Edition, Revised and Expanded, Lyndon O. Barton 82. Fundamental Fluid Mechanics for the Practicing Engineer, James W. Murdock 83. Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second Edition, Revised and Expanded, P. K. Mallick 84. Numerical Methods for Engineering Applications, Edward R. Champion, Jr.
- 11. 85. Turbomachinery: Basic Theory and Applications, Second Edition, Revised and Expanded, Earl Logan, Jr. 86. Vibrations of Shells and Plates: Second Edition, Revised and Expanded, Werner Soedel 87. Steam Plant Calculations Manual: Second Edition, Revised and Expanded, V. Ganapathy 88. Industrial Noise Control: Fundamentals and Applications, Second Edition, Revised and Expanded, Lewis H. Bell and Douglas H. Bell 89. Finite Elements: Their Design and Performance, Richard H. MacNeal 90. Mechanical Properties of Polymers and Composites: Second Edition, Revised and Expanded, Lawrence E. Nielsen and Robert F. Landel 91. Mechanical Wear Prediction and Prevention, Raymond G. Bayer 92. Mechanical Power Transmission Components, edited by David W. South and Jon R. Mancuso 93. Handbook of Turbomachinery, edited by Earl Logan, Jr. 94. Engineering Documentation Control Practices and Procedures, Ray E. Monahan 95. Refractory Linings Thermomechanical Design and Applications, Charles A. Schacht 96. Geometric Dimensioning and Tolerancing: Applications and Techniques for Use in Design, Manufacturing, and Inspection, James D. Meadows 97. An Introduction to the Design and Behavior of Bolted Joints: Third Edition, Revised and Expanded, John H. Bickford 98. Shaft Alignment Handbook: Second Edition, Revised and Expanded, John Piotrowski 99. Computer-Aided Design of Polymer-Matrix Composite Structures, edited by Suong Van Hoa 100. Friction Science and Technology, Peter J. Blau 101. Introduction to Plastics and Composites: Mechanical Properties and Engineering Applications, Edward Miller 102. Practical Fracture Mechanics in Design, Alexander Blake 103. Pump Characteristics and Applications, Michael W. Volk 104. Optical Principles and Technology for Engineers, James E. Stewart 105. Optimizing the Shape of Mechanical Elements and Structures, A. A. Seireg and Jorge Rodriguez 106. Kinematics and Dynamics of Machinery, Vladimír Stejskal and Michael Valásek 107. Shaft Seals for Dynamic Applications, Les Horve 108. Reliability-Based Mechanical Design, edited by Thomas A. Cruse 109. Mechanical Fastening, Joining, and Assembly, James A. Speck 110. Turbomachinery Fluid Dynamics and Heat Transfer, edited by Chunill Hah 111. High-Vacuum Technology: A Practical Guide, Second Edition, Revised and Expanded, Marsbed H. Hablanian 112. Geometric Dimensioning and Tolerancing: Workbook and Answerbook, James D. Meadows 113. Handbook of Materials Selection for Engineering Applications, edited by G. T. Murray 114. Handbook of Thermoplastic Piping System Design, Thomas Sixsmith and Reinhard Hanselka
- 12. 115. Practical Guide to Finite Elements: A Solid Mechanics Approach, Steven M. Lepi 116. Applied Computational Fluid Dynamics, edited by Vijay K. Garg 117. Fluid Sealing Technology, Heinz K. Muller and Bernard S. Nau 118. Friction and Lubrication in Mechanical Design, A. A. Seireg 119. Influence Functions and Matrices, Yuri A. Melnikov 120. Mechanical Analysis of Electronic Packaging Systems, Stephen A. McKeown 121. Couplings and Joints: Design, Selection, and Application, Second Edition, Revised and Expanded, Jon R. Mancuso 122. Thermodynamics: Processes and Applications, Earl Logan, Jr. 123. Gear Noise and Vibration, J. Derek Smith 124. Practical Fluid Mechanics for Engineering Applications, John J. Bloomer 125. Handbook of Hydraulic Fluid Technology, edited by George E. Totten 126. Heat Exchanger Design Handbook, T. Kuppan 127. Designing for Product Sound Quality, Richard H. Lyon 128. Probability Applications in Mechanical Design, Franklin E. Fisher and Joy R. Fisher 129. Nickel Alloys, edited by Ulrich Heubner 130. Rotating Machinery Vibration: Problem Analysis and Troubleshooting, Maurice L. Adams, Jr. 131. Formulas for Dynamic Analysis, Ronald L. Huston and C. Q. Liu 132. Handbook of Machinery Dynamics, Lynn L. Faulkner and Earl Logan, Jr. 133. Rapid Prototyping Technology: Selection and Application, Kenneth G. Cooper 134. Reciprocating Machinery Dynamics: Design and Analysis, Abdulla S. Rangwala 135. Maintenance Excellence: Optimizing Equipment Life-Cycle Decisions, edited by John D. Campbell and Andrew K. S. Jardine 136. Practical Guide to Industrial Boiler Systems, Ralph L. Vandagriff 137. Lubrication Fundamentals: Second Edition, Revised and Expanded, D. M. Pirro and A. A. Wessol 138. Mechanical Life Cycle Handbook: Good Environmental Design and Manufacturing, edited by Mahendra S. Hundal 139. Micromachining of Engineering Materials, edited by Joseph McGeough 140. Control Strategies for Dynamic Systems: Design and Implementation, John H. Lumkes, Jr. 141. Practical Guide to Pressure Vessel Manufacturing, Sunil Pullarcot 142. Nondestructive Evaluation: Theory, Techniques, and Applications, edited by Peter J. Shull 143. Diesel Engine Engineering: Thermodynamics, Dynamics, Design, and Control, Andrei Makartchouk 144. Handbook of Machine Tool Analysis, Ioan D. Marinescu, Constantin Ispas, and Dan Boboc 145. Implementing Concurrent Engineering in Small Companies, Susan Carlson Skalak 146. Practical Guide to the Packaging of Electronics: Thermal and Mechanical Design and Analysis, Ali Jamnia 147. Bearing Design in Machinery: Engineering Tribology and Lubrication, Avraham Harnoy
- 13. 148. Mechanical Reliability Improvement: Probability and Statistics for Experimental Testing, R. E. Little 149. Industrial Boilers and Heat Recovery Steam Generators: Design, Applications, and Calculations, V. Ganapathy 150. The CAD Guidebook: A Basic Manual for Understanding and Improving Computer-Aided Design, Stephen J. Schoonmaker 151. Industrial Noise Control and Acoustics, Randall F. Barron 152. Mechanical Properties of Engineered Materials, Wolé Soboyejo 153. Reliability Verification, Testing, and Analysis in Engineering Design, Gary S. Wasserman 154. Fundamental Mechanics of Fluids: Third Edition, I. G. Currie 155. Intermediate Heat Transfer, Kau-Fui Vincent Wong 156. HVAC Water Chillers and Cooling Towers: Fundamentals, Application, and Operation, Herbert W. Stanford III 157. Gear Noise and Vibration: Second Edition, Revised and Expanded, J. Derek Smith 158. Handbook of Turbomachinery: Second Edition, Revised and Expanded, edited by Earl Logan, Jr. and Ramendra Roy 159. Piping and Pipeline Engineering: Design, Construction, Maintenance, Integrity, and Repair, George A. Antaki 160. Turbomachinery: Design and Theory, Rama S. R. Gorla and Aijaz Ahmed Khan 161. Target Costing: Market-Driven Product Design, M. Bradford Clifton, Henry M. B. Bird, Robert E. Albano, and Wesley P. Townsend 162. Fluidized Bed Combustion, Simeon N. Oka 163. Theory of Dimensioning: An Introduction to Parameterizing Geometric Models, Vijay Srinivasan 164. Handbook of Mechanical Alloy Design, edited by George E. Totten, Lin Xie, and Kiyoshi Funatani 165. Structural Analysis of Polymeric Composite Materials, Mark E. Tuttle 166. Modeling and Simulation for Material Selection and Mechanical Design, edited by George E. Totten, Lin Xie, and Kiyoshi Funatani 167. Handbook of Pneumatic Conveying Engineering, David Mills, Mark G. Jones, and Vijay K. Agarwal 168. Clutches and Brakes: Design and Selection, Second Edition, William C. Orthwein 169. Fundamentals of Fluid Film Lubrication: Second Edition, Bernard J. Hamrock, Steven R. Schmid, and Bo O. Jacobson 170. Handbook of Lead-Free Solder Technology for Microelectronic Assemblies, edited by Karl J. Puttlitz and Kathleen A. Stalter 171. Vehicle Stability, Dean Karnopp 172. Mechanical Wear Fundamentals and Testing: Second Edition, Revised and Expanded, Raymond G. Bayer 173. Liquid Pipeline Hydraulics, E. Shashi Menon 174. Solid Fuels Combustion and Gasification, Marcio L. de Souza-Santos 175. Mechanical Tolerance Stackup and Analysis, Bryan R. Fischer 176. Engineering Design for Wear, Raymond G. Bayer 177. Vibrations of Shells and Plates: Third Edition, Revised and Expanded, Werner Soedel 178. Refractories Handbook, edited by Charles A. Schacht
- 14. 179. Practical Engineering Failure Analysis, Hani M. Tawancy, Anwar Ul-Hamid, and Nureddin M. Abbas 180. Mechanical Alloying and Milling, C. Suryanarayana 181. Mechanical Vibration: Analysis, Uncertainties, and Control, Second Edition, Revised and Expanded, Haym Benaroya 182. Design of Automatic Machinery, Stephen J. Derby 183. Practical Fracture Mechanics in Design: Second Edition, Revised and Expanded, Arun Shukla 184. Practical Guide to Designed Experiments, Paul D. Funkenbusch 185. Gigacycle Fatigue in Mechanical Practive, Claude Bathias and Paul C. Paris 186. Selection of Engineering Materials and Adhesives, Lawrence W. Fisher 187. Boundary Methods: Elements, Contours, and Nodes, Subrata Mukherjee and Yu Xie Mukherjee 188. Rotordynamics, Agnieszka (Agnes) Muszńyska 189. Pump Characteristics and Applications: Second Edition, Michael W. Volk 190. Reliability Engineering: Probability Models and Maintenance Methods, Joel A. Nachlas 191. Industrial Heating: Principles, Techniques, Materials, Applications, and Design, Yeshvant V. Deshmukh 192. Micro Electro Mechanical System Design, James J. Allen 193. Probability Models in Engineering and Science, Haym Benaroya and Seon Han 194. Damage Mechanics, George Z. Voyiadjis and Peter I. Kattan 195. Standard Handbook of Chains: Chains for Power Transmission and Material Handling, Second Edition, American Chain Association and John L. Wright, Technical Consultant 196. Standards for Engineering Design and Manufacturing, Wasim Ahmed Khan and Abdul Raouf S.I. 197. Maintenance, Replacement, and Reliability: Theory and Applications, Andrew K. S. Jardine and Albert H. C. Tsang 198. Finite Element Method: Applications in Solids, Structures, and Heat Transfer, Michael R. Gosz 199. Microengineering, MEMS, and Interfacing: A Practical Guide, Danny Banks 200. Fundamentals of Natural Gas Processing, Arthur J. Kidnay and William Parrish 201. Optimal Control of Induction Heating Processes, Edgar Rapoport and Yulia Pleshivtseva 202. Practical Plant Failure Analysis: A Guide to Understanding Machinery Deterioration and Improving Equipment Reliability, Neville W. Sachs, P.E. 203. Shaft Alignment Handbook, Third Edition, John Piotrowski 204. Advanced Vibration Analysis , S. Graham Kelly 205. Principles of Composite Materials Mechanics, Second Edition, Ronald F. Gibson 206. Applied Combustion, Second Edition, Eugene L. Keating 207. Introduction to the Design and Behavior of Bolted Joints, Fourth Edition: Non-Gasketed Joints, John H. Bickford
- 15. 208. Analytical and Approximate Methods in Transport Phenomena, Marcio L. de Souza-Santos 209. Design and Optimization of Thermal Systems, Second Edition, Yogesh Jaluria 210. Friction Science and Technology: From Concepts to Applications, Second Edition, Peter J. Blau 211. Practical Guide to the Packaging of Electronics, Second Edition: Thermal and Mechanical Design and Analysis, Ali Jamnia 212. Practical Stress Analysis in Engineering Design, Third Edition, Ronald L. Huston and Harold Josephs 213. Principles of Biomechanics, Ronald L. Huston 214. Mechanical Vibration Analysis, Uncertainties, and Control, Third Edition, Haym Benaroya and Mark L. Nagurka
- 17. Mechanical Vibration Analysis, Uncertainties, and Control THIRD EDITION Haym Benaroya Rutgers University Mark L. Nagurka Marquette University CRC Press is an imprint of the Taylor & Francis Group, an informa business Boca Raton London New York
- 18. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-4200-8057-5 (Ebook) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
- 19. PREFACE Introductory Comments From the natural world to the physical world, cycles are everywhere. We live our lives according to cycles as the days turn into weeks, the weeks into months, and the months into years. Cycles repeat at regular intervals and it is this repetitiveness that underlies the concept of vibration. Humans are drawn to vibration as a source of comfort –from our earliest days being rocked to sleep to our later years rocking back and forth in a rocking chair. But, vibration can also be a source of great discomfort1 with the negative e¤ects of numbness, motion sickness, injury, and even death. Speaking subjectively, vibration can be good or bad depending on the circumstance. When we don’ t want a cell phone to ring – an example of acoustic vibration –we put it in a mode called “vibrate.”We intentionally want it to vibrate. Yet, when our car vibrates too much we know from the shaking that something is wrong. It could be out of alignment; it could be the shock absorbers are shot; it could be the engine mounts are bad; it could be the engine is mis…ring. A trained mechanic will be able to diagnose the problem based on the vibration signature. In this case, we intentionally 1 Vibration exposure is more than just a nuisance. It can be a serious health hazard. Constant exposure to vibration has been known to cause a range of medical problems such as back pain, carpal tunnel syndrome, and vascular disorders. Vibration related injury is especially prevalent in occupations that require outdoor work, such as construction, farming, transportation, shipping, and forestry. There are two classi…cations for vibration exposure: whole-body vibration and hand and arm vibration. Whole-body vibration is vibration transmitted to the entire body via the seat or the feet, or both, often through driving or riding in vehicles (including trucks, tractors, trains, and o¤-road vehicles) or through standing on vibrating ‡oors (near power presses in a stamping plant or near vibrating heavy machinery, for example; pumps, compressors, air handling units and other equipment all contribute to the excitation of the ‡oors). Hand-and-arm vibration, on the other hand, is limited to the hands and arms and usually results from the use of power hand tools (reciprocating and impact tools, jackhammers, grinders, woodchippers, for example) and from vehicle controls. iii
- 20. iv want to eliminate the vibration, although we know the best we can do is minimize it. Vibration is pervasive. In fact, it is challenging to …nd examples that are not related to vibration. Applications of vibration cross disparate dis- ciplines, well beyond engineering. The following list is only a subset: biology (pulse rate, breathing rate, biorhythms, balance, tremors, just to name a few2 ) physics (waves, sound, quantum mechanics) chemistry (atomic vibration,3 spectroscopy) astronomy (planetary orbits,4 sunspot cycles) geology (seismic tremors, earthquakes, volcanic eruptions) oceanography (ocean waves, deep sea currents) meteorology (climate and weather cycles) zoology (predator-prey models of animal populations, host- parasite cycles, ecosystem cycles, among many others5 ) psychology (seasonal cycles in behavior, sleep cycles, manic- depressive cycles) economics (…nancial cycles, business cycles) agronomy (agricultural cycles) history (war and peace cycles, governance style cycles) religion (holidays, life-cycle events) philosophy (cycles in Eastern philosophy) parapsychology (astrological cycles) The word vibration is a common English word that means motion in oscillation. In a mechanical system, vibration can be viewed as a give-and- take (tug-of-war) between forces tending toward a balance. The forces are …ghting each other, causing motion that see-saws back and forth, all the 2 Almost everything in the body is rhythmic. ECG and EEG signals are rhythmic for a healthy person. Nerve action-potentials are cyclic. Eye blinking is cyclic, although the rate is not constant. Some rhythms in the body can be varied; many cannot. 3 At an atomic level vibration means there is temperature. 4 A year is the time for the Earth to rotate about the Sun once. A month is the time for the Moon to rotate about the Earth once. A day is the time for the Earth to rotate about its axis once. 5 There are many interesting examples: snakes move by and sense vibration, dogs detect danger by vibration, hummingbird wings ‡ap at known frequencies.
- 21. v time trying to achieve equilibrium. This simplistic explanation is developed in much more technical rigor in this book. We will learn that vibration occurs in a dynamic system that has at least two independent energy storage elements. We will develop models for vibration starting with a mass –which stores kinetic energy –and a spring – which stores potential energy. It is the interplay between the energies of dynamic systems that is at the root of vibration, even if we might not normally think about it this way. We close these introductory remarks with a fact of life. Vibration is life.6 The absence of vibration is death. The more vibration, the more life.7 The less vibration, the less life.8 We wish you, the reader, a healthy, meaningful and happy life, something that can only happen if it is …lled with vibration! Another Vibration Book? The decision that the profession needs another textbook on any subject must be made with great humility. That we have come to such a conclusion is in no way meant to be a rejection of other books. In fact, other books o¤er ideas and context that we do not. We have chosen to write this book in the format, content, and depth of description that we would have liked when we learned the subject for the …rst time. Audience Engineering requires several skills, including two which are most fundamen- tal: (i) the ability to read9 well and (ii) a knowledge of mathematics.10 We have written the book assuming that the reader has mastered the …rst skill and has a basic knowledge of dynamics, mechanics of materials, 6 How do you know if a person is alive? You check for a pulse, you check if they are breathing. Similarly, in the inanimate world, the presence of vibration tells us if something is working. How do you know if a car is running? You check for engine vibration or noise from the engine and vehicle. 7 The garment industry makes a signi…cant pro…t based on clothes that ensure unmen- tionable vibrations of people’ s parts as they walk. (We decided to spare the reader much more obvious examples.) 8 Health is measured by vibrations in normal ranges. Illness is identi…ed by vibrations out of the normal ranges, typically slowing (falling pulse, temperature dropping) but sometimes growing (racing pulse). 9 Without the ability to read the engineer is doomed. We encourage you to develop the habit of reading technical material with passion. Only through reading will you be able to conquer new material and truly learn it. We believe in reading. 10 Without a mastery of mathematics, you will …nd yourself handicapped in becoming and working as an engineer. (You also will be challenged in dealing with your personal …nances.)
- 22. vi di¤erential equations, and some knowledge of matrix algebra. A review of some relevant mathematics is presented in the Appendix. Following our belief that textbooks written for students should present material with su¢ cient detail to be followed easily, we have included sig- ni…cant details in the formulations and in the explanations. The book is written at the level of the senior engineering student and intended for both undergraduate and graduate students (in mechanical, civil, aerospace, and other engineering departments). Although written primarily for use as a textbook for engineering stu- dents, it is also a useful reference for practicing engineers. The material is organized so that considerable ‡ exibility is o¤ered in arranging for course level, content, and for self-study. A considerable amount of thought, feedback, and e¤ort has gone into preparing this revision. We have tried to make it straightforward to read and follow. We do not wish to imply, however, that the reader can delve into this book as if it were a novel. To derive any bene…t from it, each page must be studied slowly and carefully. Coverage The purpose of this textbook is to present comprehensive coverage of the fundamental principles of vibration theory, with emphasis on the application of these principles to practical engineering problems. In dealing with the subject of vibration, the engineer must also consider the option of vibration control as well as the e¤ects of uncertainties in the analysis. As such, this book presents the subject of modeling of uncertainties and vibration control as an integral part of vibration. Of course, this is a text on vibration, and for extensive and in-depth studies on randomness and control specialized texts should be sought. Revisions There are many changes and additions to this third edition. They are too numerous to list, but brie‡ y, the written word has been examined many times to make it more readable and clear. The mathematics has been clar- i…ed and more details presented where viewed as necessary. Interesting example problems and homework problems have been added, along with respective explanatory …gures. All these taken together have made this a new book, not just a minor change of the previous one. The material on vibration controls has been modi…ed extensively. Although a signi…cant portion of the text has been revised and expanded, no major changes have been made in the arrangement or scope since the
- 23. vii earlier editions. In rewriting this book our objective has been to present the subject in a clear and thorough way. We hope that we have succeeded. Examples and Problems The book has many examples. They have been carefully chosen and are presented at strategic points so that the reader will have a clearer under- standing of the subject matter. Some of the example problems are relatively simple and their purpose is to illustrate new ideas and subject matter. Some are more elaborate and designed to address more realistic and complicated problems. A wide selection of problems is provided at the end of each chapter, grouped together by section. They range from simple to challenging. Since engineers must be familiar with SI and U.S. customary systems of units, both systems are used in the examples and problems. Biographies A novel feature of the book is the inclusion of biographies of famous per- sonalities. We share these in the hope that the readers will appreciate that these individuals were human beings –like us –who faced many challenges throughout their lives. Despite their hardships (most are never known11 ) they were successful in making signi…cant contributions. We view them as role models and our teachers, even if we only know them by their contribu- tions and through their biographies. The intent of the biographical summaries is to add for the readers the essential human connection to this subject. Sadly in our eyes, students are rarely given the opportunity to read about the famous personalities who have made major contributions. (Each biography could have been many pages longer, and it was di¢ cult to edit them down to reasonable size.) Biographies are included here as a courtesy of Professors E.F. Robert- son and J.J. O’ Connor, School of Mathematical and Computer Sciences, 11 For example, Max Planck is known as the father of the quantum theory in physics. He introduced a quantum hypothesis to achieve agreement between his theoretical equations, which were based on the second law of thermodynamics, and experimental data. Planck had a long and successful career in physics, and was awarded the Nobel Prize in Physics in 1918 “in recognition of services he rendered to the advancement of physics by his discovery of energy quanta.” But, did you know that Planck’ s personal life was clouded by tragedy? His two daughters died in childbirth, one son died in World War I, and another son was executed in World War II for his part in an assassination attempt on Hitler in 1944. (Quantum Chemistry, D.A. McQuarrie, Second Edition, University Science Books, 2007.)
- 24. viii University of St. Andrews, St. Andrews, Scotland. Their web site is http://www-history.mcs.st-and.ac.uk/history/BiogIndex.html We have based the biographies in the book on those from St. Andrews and from other sources. We urge the reader to learn of the history of their profession. It is glorious. Further Comments about the Book This text is essentially self-contained. The student may start at the begin- ning and continue to the end with rare need to refer to other works, except to …nd additional perspectives on the subject. But then, no one text can cover all aspects of a subject as broad as vibration. If more details are desired, the reader will …nd additional information in other works that are cited. There is no separate list of references in this text. The footnotes serve as such attribution. They are intended to introduce the student to the relevant journal literature and to some of the very useful texts. In no way are the references meant to be all inclusive; they are only a starting point. Writing this book has been an exceptional privilege and an enormous learning experience. We have spent a signi…cant part of our professional careers learning the topics of the book. We remain life-long learners and hope we are granted the gifts of mental facility, physical stamina, and time to continue studying this subject –and engineering in general –for the rest of our lives. Instructional Options This book includes material that can be covered at two course levels, one undergraduate and one graduate. The instructor may choose a variety of options for the use of this text. It is generally possible to skip sections that do not …t with the philosophy of the instructor. A …rst course is likely to omit the more advanced subjects such as random vibration in Chapter 5 and the variational approaches of Chapter 7. A logical sequence of material has been presented in the chapters so that the instructor can leave out sections that do not …t into the particular syllabus. These omitted topics can be studied in a second course, where more advanced topics can provide a broader perspective on vibration. In particular, an undergraduate course could cover most of the introduc- tory and background Chapter 1, the single degree-of-freedom Chapters 2 to
- 25. ix 4, and Chapter 8 on multi degree-of-freedom systems. Chapter 5 on ran- domness and Chapter 6 on feedback control provide the instructor with resources that permit a customized syllabus. The second, usually graduate, course could brie‡ y review Chapters 1, 2 to 4, introduce the subjects of randomness and control in Chapters 5 and 6, and spend the most time on the variational techniques of Chapter 7, the multi degree and continuous systems of Chapters 8 to 11, and on nonlin- ear vibration and stability of Chapter 12. The choices and emphasis will depend on the level of preparation of the students and the curricular philos- ophy of the institution. A two semester sequence can cover all the material contained in this book. A Special Note to Students Like most things of meaning in life, the subject of vibration is not easy. Our goal in writing this textbook has been to help you learn the subject – but the book must be read and studied if the material is going to sink in. Nothing beats working through the examples and solving the problems to conquer the subject of vibration. Going through challenging material and struggling to understand it can be frustrating, but they are necessary steps in learning. Little would be gained if this book could be read once –like a novel – and fully absorbed without much thought. It is only through the process of grappling with fundamental concepts of vibration that you can gain a level of understanding that will make the subject meaningful. Vibrations has many practical applications and we have tried to convey that sense throughout the book. Engineers, after all, work in the real-world, solving real problems that help real people. It might seem that vibration is an abstract or theoretical discipline, especially seeing how much math there is here. Some of you may even be dismayed by the advanced level of math needed. Recognizing the value of math as a cornerstone to engineering is an important message that we hope the reader takes away. As we progress through the book, we will rely on di¤erential equations to model vibrating systems. Elementary models built of discrete components (masses, springs, dampers) will be couched in terms of ordinary di¤erential equations. Later models assuming continuous components (beams, shafts, rods) will be represented by partial di¤erential equations.
- 26. Other documents randomly have different content
- 27. gas delivery tube[15] passes whose end is immersed under water, it will be observed that on heating, a gas is formed which bubbles through the water. This gas can be easily collected, as will presently be described, and it will be found to essentially differ from air in many respects; for instance, a burning taper is extinguished in it as if it had been plunged into water. If weighing had not proved to us that some substance had been separated, the formation of the gas might easily have escaped our notice, for it is colourless and transparent like air, and is therefore evolved without any striking feature. The carbonic anhydride evolved may be weighed,[16] and it will be seen that the sum of the weights of the black copper oxide and carbonic anhydride is equal to the weight of the copper carbonate[17] originally taken, and thus by carefully following out the various stages of all chemical reactions we arrive at a confirmation of the law of the indestructibility of matter. 3. Red mercury oxide (which is formed as mercury rust by heating mercury in air) is decomposed like copper carbonate (only by heating more slowly and at a somewhat higher temperature), with the formation of the peculiar gas, oxygen. For this purpose the mercury oxide is placed in a glass tube or retort,[18] to which a gas delivery tube is attached by means of a cork. This tube is bent downwards, as shown in the drawing (Fig. 1). The open end of the gas delivery tube is immersed in a vessel filled with water, called a pneumatic trough.[19] When the gas begins to be evolved in the retort it is obliged, having no other outlet, to escape through the gas delivery tube into the water in the pneumatic trough, and therefore its evolution will be rendered visible by the bubbles coming from this tube. In heating the retort containing the mercury oxide, the air
- 28. contained in the apparatus is first partly expelled, owing to its expansion by heat, and then the peculiar gas called ‘oxygen’ is evolved, and may be easily collected as it comes off. For this purpose a vessel (an ordinary cylinder, as in the drawing) is filled quite full with water and its mouth closed; it is then inverted and placed in this position under the water in the trough; the mouth is then opened. The cylinder will remain full of water—that is, the water will remain at a higher level in it than in the surrounding vessel, owing to the atmospheric pressure. The atmosphere presses on the surface of the water in the trough, and prevents the water from flowing out of the cylinder. The mouth of the cylinder is placed over the end of the gas delivery tube,[20] and the bubbles issuing from it will rise into the cylinder and displace the water contained in it. Gases are generally collected in this manner. When a sufficient quantity of gas has accumulated in the cylinder it can be clearly shown that it is not air, but another gas which is distinguished by its capacity for vigorously supporting combustion. In order to show this, the cylinder is closed, under water, and removed from the bath; its mouth is then turned upwards, and a smouldering taper plunged into it. As is well known, a smouldering taper will be extinguished in air, but in the gas which is given off from red mercury oxide it burns clearly and vigorously, showing the property possessed by this gas for supporting combustion more energetically than air, and thus enabling it to be distinguished from the latter. It may be observed in this experiment that, besides the formation of oxygen, metallic mercury is formed, which, volatilising at the high temperature required for the reaction, condenses on the cooler parts of the retort as a mirror or in globules. Thus two substances, mercury and oxygen, are obtained by heating red mercury oxide. In this reaction, from
- 29. one substance, two new substances are produced—that is, a decomposition has taken place. The means of collecting and investigating gases were known before Lavoisier's time, but he first showed the real part they played in the processes of many chemical changes which before his era were either wrongly understood (as will be afterwards explained) or were not explained at all, but only observed in their superficial aspects. This experiment on red mercury oxide has a special significance in the history of chemistry contemporary with Lavoisier, because the oxygen gas which is here evolved is contained in the atmosphere, and plays a most important part in nature, especially in the respiration of animals, in combustion in air, and in the formation of rusts or scoriæ (earths, as they were then called) from metals—that is, of earthy substances, like the ores from which metals are extracted. 4. In order to illustrate by experiment one more example of chemical change and the application of the law of the indestructibility of matter, we will consider the reaction between common table salt and lunar caustic, which is well known from its use in cauterising wounds. By taking a clear solution of each and mixing them together, it will at once be observed that a solid white substance is formed, which settles to the bottom of the vessel, and is insoluble in water. This substance may be separated from the solution by filtering; it is then found to be an entirely different substance from either of those taken originally in the solutions. This is at once evident from the fact that it does not dissolve in water. On evaporating the liquid which passed through the filter, it will be found to contain a new substance unlike either table salt or lunar caustic, but, like them, soluble in water. Thus table salt and lunar caustic, two substances soluble in water, produced,
- 30. by their mutual chemical action, two new substances, one insoluble in water, and the other remaining in solution. Here, from two substances, two others are obtained, consequently there occurred a reaction of substitution. The water served only to convert the re-acting substances into a liquid and mobile state. If the lunar caustic and salt be dried[21] and weighed, and if about 58½ grams[22] of salt and 170 grams of lunar caustic be taken, then 143½ grams of insoluble silver chloride and 85 grams of sodium nitrate will be obtained. The sum of the weights of the re-acting and resultant substances are seen to be similar and equal to 228½ grams, which necessarily follows from the law of the indestructibility of matter. Accepting the truth of the above law, the question naturally arises as to whether there is any limit to the various chemical transformations, or are they unrestricted in number—that is to say, is it possible from a given substance to obtain an equivalent quantity of any other substance? In other words, does there exist a perpetual and infinite change of one kind of material into every other kind, or is the cycle of these transformations limited? This is the second essential problem of Chemistry, a question of quality of matter, and one, it is evident, which is more complicated than the question of quantity. It cannot be solved by a mere superficial glance at the subject. Indeed, on seeing how all the varied forms and colours of plants are built up from air and the elements of the soil, and how metallic iron can be transformed into colours such as inks and Prussian blue, we might be led to think that there is no end to the qualitative changes to which matter is susceptible. But, on the other hand, the experiences of everyday life compel us to acknowledge that food cannot be made out of a stone, or gold out of copper. Thus a definite
- 31. answer can only be looked for in a close and diligent study of the subject, and the problem has been resolved in different way at different times. In ancient times the opinion most generally held was that everything visible was composed of four elements—Air, Water, Earth, and Fire. The origin of this doctrine can be traced far back into the confines of Asia, whence it was handed down to the Greeks, and most fully expounded by Empedocles, who lived before 460 B.C. This doctrine was not the result of exact research, but apparently owes its origin to the clear division of bodies into gases (like air), liquids (like water), and solids (like the earth). The Arabs appear to have been the first who attempted to solve the question by experimental methods, and they introduced, through Spain, the taste for the study of similar problems into Europe, where from that time there appear many adepts in chemistry, which was considered as an unholy art, and called ‘alchemy.’ As the alchemists were ignorant of any exact law which could guide them in their researches, they obtained most anomalous results. Their chief service to chemistry was that they made a number of experiments, and discovered many new chemical transformations; but it is well known how they solved the fundamental problem of chemistry. Their view may be taken as a positive acknowledgment of the infinite transmutability of matter, for they aimed at discovering the Philosopher's Stone, capable of converting everything into gold and diamonds, and of making the old young again. This solution of the question was afterwards completely overthrown, but it must not, for this reason, be thought that the hopes held by the alchemists were only the fruit of their imaginations. The first chemical experiments might well lead them to their conclusions. They took, for instance, the bright metallic mineral galena, and extracted metallic lead from it.
- 32. Thus they saw that from a metallic substance which is unfitted for use they could obtain another metallic substance which is ductile and valuable for many technical purposes. Furthermore, they took this lead and obtained silver, a still more valuable metal, from it. Thus they might easily conclude that it was possible to ennoble metals by means of a whole series of transmutations—that is to say, to obtain from them those which are more and more precious. Having got silver from lead, they assumed that it would be possible to obtain gold from silver. The mistake they made was that they never weighed or measured the substances used or produced in their experiments. Had they done so, they would have learnt that the weight of the lead was much less than that of the galena from which it was obtained, and the weight of the silver infinitesimal compared with that of the lead. Had they looked more closely into the process of the extraction of the silver from lead (and silver at the present time is chiefly obtained from the lead ores) they would have seen that the lead does not change into silver, but that it only contains a certain small quantity of it, and this amount having once been separated from the lead it cannot by any further operation give more. The silver which the alchemists extracted from the lead was in the lead, and was not obtained by a chemical change of the lead itself. This is now well known from experiment, but the first view of the nature of the process was very likely to be an erroneous one.[23] The methods of research adopted by the alchemists could give but little success, for they did not set themselves clear and simple questions whose answers would aid them to make further progress. Thus though they did not arrive at any exact law, they left nevertheless numerous and useful experimental data as an inheritance to chemistry; they investigated, in particular,
- 33. the transformations proper to metals, and for this reason chemistry was for long afterwards entirely confined to the study of metallic substances. In their researches, the alchemists frequently made use of two chemical processes which are now termed ‘reduction’ and ‘oxidation.’ The rusting of metals, and in general their conversion from a metallic into an earthy form, is called ‘oxidation,’ whilst the extraction of a metal from an earthy substance is called ‘reduction.’ Many metals—for instance, iron, lead, and tin—are oxidised by heating in air alone, and may be again reduced by heating with carbon. Such oxidised metals are found in the earth, and form the majority of metallic ores. The metals, such as tin, iron, and copper, may be extracted from these ores by heating them together with carbon. All these processes were well studied by the alchemists. It was afterwards shown that all earths and minerals are formed of similar metallic rusts or oxides, or of their combinations. Thus the alchemists knew of two forms of chemical changes: the oxidation of metals and the reduction of the oxides so formed into metals. The explanation of the nature of these two classes of chemical phenomena was the means for the discovery of the most important chemical laws. The first hypothesis on their nature is due to Becker, and more particularly to Stahl, a surgeon to the King of Prussia. Stahl writes in his ‘Fundamenta Chymiæ,’ 1723, that all substances consist of an imponderable fiery substance called ‘phlogiston’ (materia aut principium ignis non ipse ignis), and of another element having particular properties for each substance. The greater the capacity of a body for oxidation, or the more combustible it is, the richer it is in phlogiston. Carbon contains it in great abundance. In oxidation or combustion phlogiston is emitted, and in reduction it is
- 34. consumed or enters into combination. Carbon reduces earthy substances because it is rich in phlogiston, and gives up a portion of its phlogiston to the substance reduced. Thus Stahl supposed metals to be compound substances consisting of phlogiston and an earthy substance or oxide. This hypothesis is distinguished for its very great simplicity, and for this and other reasons it acquired many supporters.[24] Fig. 3.—Lavoisier's apparatus for determining the composition of air and the reason of metals increasing in weight when they are calcined in air. Lavoisier proved by means of the balance that every case of rusting of metals or oxidation, or of combustion, is accompanied by an increase in weight at the expense of the atmosphere. He formed, therefore, the natural opinion that the heavier substance is more complex than the lighter one. [25] Lavoisier's celebrated experiment, made in 1774, gave indubitable support to his opinion, which in many respects was contradictory to Stahl's doctrine. Lavoisier poured four
- 35. ounces of pure mercury into a glass retort (fig. 3), whose neck was bent as shown in the drawing and dipped into the vessel R S, also full of mercury. The projecting end of the neck was covered with a glass bell-jar P. The weight of all the mercury taken, and the volume of air remaining in the apparatus, namely, that in the upper portion of the retort, and under the bell-jar, were determined before beginning the experiment. It was most important in this experiment to know the volume of air in order to learn what part it played in the oxidation of the mercury, because, according to Stahl, phlogiston is emitted into the air, whilst, according to Lavoisier, the mercury in oxidising absorbs a portion of the air; and consequently it was absolutely necessary to determine whether the amount of air increased or decreased in the oxidation of the metal. It was, therefore, most important to measure the volume of the air in the apparatus both before and after the experiment. For this purpose it was necessary to know the total capacity of the retort, the volume of the mercury poured into it, the volume of the bell-jar above the level of the mercury, and also the temperature and pressure of the air at the time of its measurement. The volume of air contained in the apparatus and isolated from the surrounding atmosphere could be determined from these data. Having arranged his apparatus in this manner, Lavoisier heated the retort holding the mercury for a period of twelve days at a temperature near the boiling point of mercury. The mercury became covered with a quantity of small red scales; that is, it was oxidised or converted into an earth. This substance is the same mercury oxide which has already been mentioned (example 3). After the lapse of twelve days the apparatus was cooled, and it was then seen that the volume of the air in the apparatus had diminished during the time of the experiment.
- 36. This result was in exact contradiction to Stahl's hypothesis. Out of 50 cubic inches of air originally taken, there only remained 42. Lavoisier's experiment led to other equally important results. The weight of the air taken decreased by as much as the weight of the mercury increased in oxidising; that is, the portion of the air was not destroyed, but only combined with mercury. This portion of the air may be again separated from the mercury oxide and has, as we saw (example 3), properties different from those of air. It is called ‘oxygen.’ That portion of the air which remained in the apparatus and did not combine with the mercury does not oxidise metals, and cannot support either combustion or respiration, so that a lighted taper is immediately extinguished if it be dipped into the gas which remains in the bell-jar. ‘It is extinguished in the residual gas as if it had been plunged into water,’ writes Lavoisier in his memoirs. This gas is called ‘nitrogen.’ Thus air is not a simple substance, but consists of two gases, oxygen and nitrogen, and therefore the opinion that air is an elementary substance is erroneous. The oxygen of the air is absorbed in combustion and the oxidation of metals, and the earths produced by the oxidation of metals are substances composed of oxygen and a metal. By mixing the oxygen with the nitrogen the same air as was originally taken is re-formed. It has also been shown by direct experiment that on reducing an oxide with carbon, the oxygen contained in the oxide is transferred to the carbon, and gives the same gas that is obtained by the combustion of carbon in air. Therefore this gas is a compound of carbon and oxygen, just as the earthy oxides are composed of metals and oxygen. The many examples of the formation and decomposition of substances which are met with convince us that the majority of substances with which we have to deal are compounds
- 37. made up of several other substances. By heating chalk (or else copper carbonate, as in the second example) we obtain lime and the same carbonic acid gas which is produced by the combustion of carbon. On bringing lime into contact with this gas and water, at the ordinary temperature, we again obtain the compound, carbonate of lime, or chalk. Therefore chalk is a compound. So also are those substances from which it may be built up. Carbonic anhydride is formed by the combination of carbon and oxygen; and lime is produced by the oxidation of a certain metal called ‘calcium.’ By resolving substances in this manner into their component parts, we arrive at last at such as are indivisible into two or more substances by any means whatever, and which cannot be formed from other substances. All we can do is to make such substances combine together to act on other substances. Substances which cannot be formed from or decomposed into others are termed simple substances (elements). Thus all homogeneous substances may be classified into simple and compound substances. This view was introduced and established as a scientific fact during the lifetime of Lavoisier. The number of these elements is very small in comparison with the number of compound substances which are formed by them. At the present time, only seventy elements are known with certainty to exist. Some of them are very rarely met with in nature, or are found in very small quantities, whilst the existence of others is still doubtful. The number of elements with whose compounds we commonly deal in everyday life is very small. Elements cannot be transmuted into one another—at least up to the present not a single case of such a transformation has been met with; it may therefore be said that, as yet, it is impossible to transmute one metal into another. And as yet, notwithstanding the number of attempts which have been
- 38. made in this direction, no fact has been discovered which could in any way support the idea of the complexity of such well-known elements[26] as oxygen, iron, sulphur, &c. Therefore, from its very conception, an element is not susceptible to reactions of decomposition.[27] The quantity, therefore, of each element remains constant in all chemical changes: a fact which may be deduced as a consequence of the law of the indestructibility of matter, and of the conception of elements themselves. Thus the equation expressing the law of the indestructibility of matter acquires a new and still more important signification. If we know the quantities of the elements which occur in the re-acting substances, and if from these substances there proceed, by means of chemical changes, a series of new compound substances, then the latter will together contain the same quantity of each of the elements as there originally existed in the re-acting substances. The essence of chemical change is embraced in the study of how, and with what substances, each element is combined before and after change. In order to be able to express various chemical changes by equations, it has been agreed to represent each element by the first or some two letters of its (Latin) name. Thus, for example, oxygen is represented by the letter O; nitrogen by N; mercury (hydrargyrum) by Hg; iron (ferrum) by Fe; and so on for all the elements, as is seen in the tables on page 24. A compound substance is represented by placing the symbols representing the elements of which it is made up side by side. For example, red mercury oxide is represented by HgO, which shows that it is composed of oxygen and mercury. Besides this, the symbol of every element corresponds with a certain relative quantity of it by weight, called its ‘combining’ weight,
- 39. or the weight of an atom; so that the chemical formula of a compound substance not only designates the nature of the elements of which it is composed, but also their quantitative proportion. Every chemical process may be expressed by an equation composed of the formulæ corresponding with those substances which take part in it and are produced by it. The amount by weight of the elements in every chemical equation must be equal on both sides of the equation, since no element is either formed or destroyed in a chemical change. On pages 24, 25, and 26 a list of the elements, with their symbols and combining or atomic weights, is given, and we shall see afterwards on what basis the atomic weights of elements are determined. At present we will only point out that a compound containing the elements A and B is designated by the formula An Bm, where m and n are the coefficients or multiples in which the combining weights of the elements enter into the composition of the substance. If we represent the combining weight of the substance A by a and that of the substance B by b, then the composition of the substance An Bm will be expressed thus: it contains na parts by weight of the substance A and mb parts by weight of the substance B, and consequently 100 parts of our compound contain na 100 na + mb percentage parts by weight of the substance A and mb 100 na + mb of the substance B. It is evident that as a formula shows the relative amounts of all the elements contained in a compound, the actual weights of the elements contained in a given weight of a compound may be calculated from its formula. For example, the formula NaCl of
- 40. table salt shows (as Na = 23 and Cl = 35·5) that 58·5 lbs. of salt contain 23 lbs. of sodium and 35·5 lbs. of chlorine, and that 100 parts of it contain 39·3 per cent. of sodium and 60·7 per cent. of chlorine. What has been said above clearly limits the province of chemical changes, because from substances of a given kind there can be obtained only such as contain the same elements. Even with this limitation, however, the number of possible combinations is infinitely great. Only a comparatively small number of compounds have yet been described or subjected to research, and any one working in this direction may easily discover new compounds which had not before been obtained. It often happens, however, that such newly- discovered compounds were foreseen by chemistry, whose object is the apprehension of that uniformity which rules over the multitude of compound substances, and whose aim is the comprehension of those laws which govern their formation and properties. The conception of elements having been established, the next objects of chemistry were: the determination of the properties of compound substances on the basis of the determination of the quantity and kind of elements of which they are composed; the investigation of the elements themselves; the determination of what compound substances can be formed from each element and the properties which these compounds show; and the apprehension of the nature of the connection between the elements in different compounds. An element thus serves as the starting point, and is taken as the primary conception on which all other substances are built up. When we state that a certain element enters into the composition of a given compound (when we say, for instance,
- 41. that mercury oxide contains oxygen) we do not mean that it contains oxygen as a gaseous substance, but only desire to express those transformations which mercury oxide is capable of making; that is, we wish to say that it is possible to obtain oxygen from mercury oxide, and that it can give up oxygen to various other substances; in a word, we desire only to express those transformations of which mercury oxide is capable. Or, more concisely, it may be said that the composition of a compound is the expression of those transformations of which it is capable. It is useful in this sense to make a clear distinction between the conception of an element as a separate homogeneous substance, and as a material but invisible part of a compound. Mercury oxide does not contain two simple bodies, a gas and a metal, but two elements, mercury and oxygen, which, when free, are a gas and a metal. Neither mercury as a metal nor oxygen as a gas is contained in mercury oxide; it only contains the substance of these elements, just as steam only contains the substance of ice, but not ice itself, or as corn contains the substance of the seed, but not the seed itself. The existence of an element may be recognised without knowing it in the uncombined state, but only from an investigation of its combinations, and from the knowledge that it gives, under all possible conditions, substances which are unlike other known combinations of substances. Fluorine is an example of this kind. It was for a long time unknown in a free state, and nevertheless was recognised as an element because its combinations with other elements were known, and their difference from all other similar compound substances was determined. In order to grasp the difference between the conception of the visible form of an element as we know it in the free state, and of the intrinsic element (or ‘radicle,’ as Lavoisier called it) contained
- 42. in the visible form, it should be remarked that compound substances also combine together forming yet more complex compounds, and that they evolve heat in the process of combination. The original compound may often be extracted from these new compounds by exactly the same methods as elements are extracted from their corresponding combinations. Besides, many elements exist under various visible forms whilst the intrinsic element contained in these various forms is something which is not subject to change. Thus carbon appears as charcoal, graphite, and diamond, but yet the element carbon alone, contained in each, is one and the same. Carbonic anhydride contains carbon, and not charcoal, or graphite, or the diamond. Elements alone, although not all of them, have the peculiar lustre, opacity, malleability, and the great heat and electrical conductivity which are proper to metals and their mutual combinations. But elements are far from all being metals. Those which do not possess the physical properties of metals are called non-metals (or metalloids). It is, however, impossible to draw a strict line of demarcation between metals and non-metals, there being many intermediary substances. Thus graphite, from which pencils are manufactured, is an element with the lustre and other properties of a metal; but charcoal and the diamond, which are composed of the same substance as graphite, do not show any metallic properties. Both classes of elements are clearly distinguished in definite examples, but in particular cases the distinction is not clear and cannot serve as a basis for the exact division of the elements into two groups. The conception of elements forms the basis of chemical knowledge, and in giving a list of them at the very beginning
- 43. of our work, we wish to tabulate our present knowledge on the subject. Altogether about seventy elements are now authentically known, but many of them are so rarely met with in nature, and have been obtained in such small quantities, that we possess but a very insufficient knowledge of them. The substances most widely distributed in nature contain a very small number of elements. These elements have been more completely studied than the others, because a greater number of investigators have been able to carry on experiments and observations on them. The elements most widely distributed in nature are:— Hydrogen, H=1. In water, and in animal and vegetable organisms. Carbon, C=12. In organisms, coal, limestones. Nitrogen, N=14. In air and in organisms. Oxygen, O=16. In air, water, earth. It forms the greater part of the mass of the earth. Sodium, Na=23. In common salt and in many minerals. Magnesium, Mg=24. In sea-water and in many minerals. Aluminium, Al=27. In minerals and clay. Silicon, Si=28. In sand, minerals, and clay. Phosphorus, P=31. In bones, ashes of plants, and soil. Sulphur, S=32. In pyrites, gypsum, and in sea-water. Chlorine, Cl=35·5. In common salt, and in the salts of sea-water. Potassium, K=39. In minerals, ashes of plants, and in nitre. Calcium, Ca=40. In limestones, gypsum, and in organisms. Iron, K=56. In the earth, iron ores, and in organisms.
- 44. Besides these, the following elements, although not very largely distributed in nature, are all more or less well known from their applications to the requirements of everyday life or the arts, either in a free state or in their compounds:— Lithium, Li=7. In medicine (Li2CO3), and in photography (LiBr). Boron, B=11. As borax, B4Na2O7, and as boric anhydride, B2O3. Fluorine, F=19. As fluor spar, CaF2, and as hydrofluoric acid, HF. Chromium, Cr=52. As chromic anhydride, CrO3, and potassium dichromate, K2Cr2O7. Manganese,Mn=55. As manganese peroxide, MnO2, and potassium permanganate, MnKO4. Cobalt, Co=59·5. In smalt and blue glass. Nickel, Ni=59·5. For electro-plating other metals. Copper, Cu=63. The well-known red metal. Zinc, Zn=65. Used for the plates of batteries, roofing, &c. Arsenic, As=75. White arsenic (poison), As2O3. Bromine, Cu=80. A brown volatile liquid; sodium bromide, NaBr. Strontium, Sr=87. In coloured fires (SrN2O6). Silver, Ag=109. The well-known white metal. Cadmium, Cd=112. In alloys. Yellow paint (CdS). Tin, Sn=119. The well-known metal. Antimony, Sb=120. In alloys such as type metal. Iodine, I=127. In medicine and photography; free, and as KI.
- 45. Barium, Ba=137. “Permanent white,” and as an adulterant in white lead, and in heavy spar, BaSO4. Platinum, Pt=196. Well-known metals. Gold, Au=197. Mercury, Hg=200. Lead, Pb=207. Bismuth, Bi=209. In medicine and fusible alloys. Uranium, U=239. In green fluorescent glass. The compounds of the following metals and semi-metals have fewer applications, but are well known, and are somewhat frequently met with in nature, although in small quantities:— Beryllium, Be=9. Palladium,Pd=107. Titanium, Ti=48. Cerium, Ce=140. Vanadium, V=51. Tungsten, W=184. Selenium, Se=79. Osmium, Os=192. Zirconium, Zr=91. Iridium, Ir=193. Molybdenum,Mo=96. Thallium, Tl=204. The following rare metals are still more seldom met with in nature, but have been studied somewhat fully:— Scandium, Sc=44. Germanium,Ge=72. Gallium, Ga=70. Rubidium, Rb=86. Yttrium, Y=89. Cæsium, Cs=133. Niobium, Nb=94. Lanthanum, La=138. Ruthenium,Ru=102. Didymium, Di=142. Rhodium, Rh=103. Ytterbium, Yb=173. Indium, In=114. Tantalum, Ta=183. Tellurium, Te=125. Thorium, Th=232.
- 46. Besides these 66 elements there have been discovered:— Erbium, Terbium, Samarium, Thullium, Holmium, Mosandrium, Phillipium, and several others. But their properties and combinations, owing to their extreme rarity, are very little known, and even their existence as independent substances[28] is doubtful. It has been incontestably proved from observations on the spectra of the heavenly bodies that many of the commoner elements (such as H, Na, Mg, Fe) occur on the far distant stars. This fact confirms the belief that those forms of matter which appear on the earth as elements are widely distributed over the entire universe. But we do not yet know why, in nature, the mass of some elements should be greater than that of others.[28 bis] The capacity of each element to combine with one or another element, and to form compounds with them which are in a greater or less degree prone to give new and yet more complex substances, forms the fundamental character of each element. Thus sulphur easily combines with the metals, oxygen, chlorine, or carbon, whilst gold and silver enter into combinations with difficulty, and form unstable compounds, which are easily decomposed by heat. The cause or force which induces the elements to enter into chemical change must be considered, as also the cause which holds different substances in combination—that is, which endues the substances formed with their particular degree of stability. This cause or force is called affinity (affinitas, affinité, Verwandtschaft), or chemical affinity.[29] Since this force must be regarded as exclusively an attractive force, like gravity, many writers (for instance, Bergmann at the end of the last, and Berthollet at the beginning of this, century) supposed
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