Solution Manual for Industrial Automated Systems Instrumentation and Motion Control, 1st Edition
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- 5. NDUSTRIAL AUTOMATED SYSTEMS: INSTRUMENTATION AND MOTION CONTROL, will provide readers with state-of-the art coverage of the full spectrum of industrial maintenance and control, from servomechanisms to instrumentation. They will learn about components, circuits, instruments, control techniques, calibration, tuning and programming associated with industrial automated systems. INDUSTRIAL AUTOMATED SYSTEMS: INSTRUMENTATION AND MOTION CONTROL, focuses on operation, rather than mathematical design concepts. It is formatted into sections so that it can be used to learn a variety of subjects, such as electrical motors, sensors, variable speed drives, programmable logic controllers, servomechanisms, and various instrumentation and process. This book also offers readers a broader coverage of industrial maintenance and automation information than other books and provides them with an extensive collection of supplements, including a lab manual and two hundred animated multimedia lessons on CD. 1. Contents 2. Lab.Source Contents 3. Preface 4. Section 1: Industrial Control Overview 5. Ch 1: Introduction to Industrial Control Systems 6. Introduction 7. 1-1 Industrial Control Classifications 8. 1-2 Elements of Open- and Closed-Loop Systems 9. 1-3 Feedback Control 10. 1-4 Practical Feedback Application 11. 1-5 Dynamic Response of a Closed-Loop System 12. 1-6 Feed-Forward Control 13. Problems 14. Ch 2: Interfacing Devices 15. Introduction 16. 2-1 Fundamental Operational Amplifiers 17. 2-2 Signal Processors
- 6. 18. 2-3 Comparator Devices 19. 2-4 Optoelectronic Interface Devices 20. 2-5 Digital-to-Analog Converters 21. 2-6 Analog-to-Digital Converters 22. 2-7 Timing Devices 23. Problems 24. Ch 3: Thyristors 25. Introduction 26. 3-1 Silicon-Controlled Rectifiers 27. 3-2 Unijunction Transistors 28. 3-3 Diac 29. 3-4 Triac 30. 3-5 IGBTs 31. Problems 32. Section 2: The Controller 33. Ch 4: The Controller Operation 34. Introduction 35. 4-1 Control Modes 36. 4-2 On-Off Control 37. 4-3 Proportional Control 38. 4-4 Proportional-Integral Control 39. 4-5 Proportional-Integral-Derivative Control 40. 4-6 Time-Proportioning Control 41. 4-7 Time-Proportioning Circuit 42. Problems 43. Section 3: Electric Motors 44. Ch 5: DC Motors 45. Introduction 46. 5-1 Principles of Operation 47. 5-2 Rotary Motion 48. 5-3 Practical DC Motors 49. 5-4 Control of Field Flux 50. 5-5 Counterelectromotive Force 51. 5-6 Armature Reaction 52. 5-7 Motor Selection 53. 5-8 Interrelationships 54. 5-9 Basic Motor Construction 55. 5-10 Motor Classifications 56. 5-11 Coil Terminal Identification 57. Problems 58. Ch 6: AC Motors 59. Introduction 60. 6-1 Fundamental Operation 61. 6-2 Stator Construction and Operation 62. 6-3 Types of AC Motors 63. 6-4 Single-Phase Induction Motors
- 7. 64. 6-5 Resistance-Start Induction-Run Motor 65. 6-6 Capacitor-Start Induction-Run Motor 66. 6-7 Shaded-Pole Motor 67. 6-8 Troubleshooting Split-Phase AC Motors 68. 6-9 Universal Motors 69. 6-10 Three-Phase Motors 70. 6-11 Induction Motor 71. 6-12 Wound-Rotor Motor 72. 6-13 Synchronous Motor 73. 6-14 Motor Nameplate 74. Problems 75. Ch 7: Servo Motors 76. Introduction 77. 7-1 DC Servo Motors 78. 7-2 Wound Armature PM Motor 79. 7-3 Moving Coil Motor 80. 7-4 Brushless DC Motors 81. 7-5 Stepper Motors 82. 7-6 Permanent Magnet Stepper Motor 83. 7-7 Variable Reluctance Stepper Motor 84. 7-8 AC Servo Motors 85. Problems 86. Section 4: Variable-Speed Drives 87. Ch 8: DC Drives 88. Introduction 89. 8-1 DC Drive Fundamentals 90. 8-2 Variable-Voltage DC Drive 91. 8-3 Motor Braking 92. Problems 93. Ch 9: AC Drives 94. Introduction 95. 9-1 AC Drive Fundamentals 96. 9-2 AC Drive System 97. 9-3 Drive Controller Internal Circuitry 98. 9-4 Circuit Operation of the AC Drive 99. 9-5 Flux Vector Control 100. 9-6 PWM Control Methods 101. 9-7 Control Panel Inputs and Drive Functions 102. 9-8 Inverter Self-Protection Function 103. 9-9 Motor Braking 104. 9-10 Four-Quadrant Operation of AC Motors 105. 9-11 AC Drive Selection 106. 9-12 Motors Driven by AC Drives 107. Problems 108. Section 5: Process Control and Instrumentation 109. Ch 10: Pressure Systems
- 8. 110. Introduction 111. 10-1 Pressure Laws 112. 10-2 Properties of a Liquid 113. 10-3 Properties of a Gas 114. 10-4 Pressure Measurement Scales 115. 10-5 Pressure Measurement Instruments 116. 10-6 Nonelectrical Pressure Sensors 117. 10-7 Electronic Pressure Sensors 118. 10-8 Pressure Control Systems 119. Problems 120. Ch 11: Temperature Control 121. Introduction 122. 11-1 Fundamentals of Temperature 123. 11-2 Thermal Control Systems 124. 11-3 Thermodynamic Transfer 125. 11-4 Thermal Energy Source 126. 11-5 Temperature Measurements 127. 11-6 Temperature-Indicating Devices 128. 11-7 Electronic Sensors 129. Problems 130. Ch 12: Flow Control 131. Introduction 132. 12-1 Systems Concepts 133. 12-2 Flow Units of Measurement 134. 12-3 Solid Flow Measurement 135. 12-4 Fluid Flow Measurement 136. 12-5 Electronic Sensors 137. 12-6 Flowmeter Placement 138. 12-7 Selecting a Flowmeter 139. Problems 140. Ch 13: Level-Control Systems 141. Introduction 142. 13-1 A Level-Control System 143. 13-2 Methods of Measurement 144. 13-3 Level-Measurement Methods 145. 13-4 Electronic Sensors 146. 13-5 Selecting a Level Sensor 147. Problems 148. Ch 14: Analytical Instrumentation 149. Introduction 150. 14-1 pH Measurement and Control 151. 14-2 Conductivity 152. 14-3 Combustion Analyzers and Control 153. 14-4 Humidity 154. 14-5 Sampling Measurement System 155. Problems
- 9. 156. Ch 15: Industrial Process Techniques and Instrumentation 157. Introduction 158. 15-1 Batch Processes 159. 15-2 Continuous Processes 160. 15-3 Instrumentation 161. 15-4 Measurement Devices (Sensors) 162. 15-5 Feedback Loop Interface Instruments 163. 15-6 Controllers 164. 15-7 Monitoring Instruments 165. 15-8 Manipulation Devices (The Final Control Element) 166. Problems 167. Ch 16: Instrumentation Symbology 168. Introduction 169. 16-1 General Instrument Symbols 170. 16-2 Tag Numbers 171. 16-3 Line Symbols 172. 16-4 Valve and Actuator Symbols 173. 16-5 Reading a Single Loop 174. 16-6 Information Block 175. Problems 176. Ch 17: Process-Control Methods 177. Introduction 178. 17-1 Open-Loop Control 179. 17-2 Closed-Loop Control 180. 17-3 Single-Variable Control Loop 181. 17-4 Selecting a Controller 182. 17-5 On-Off Control 183. 17-6 Continuous Control 184. 17-7 Advanced Control Techniques 185. Problems 186. Ch 18: Instrument Calibration and Controller Tuning 187. Introduction 188. 18-1 Instrument Calibration 189. 18-2 Reasons for Performing Calibrations 190. 18-3 Calibration Preparation 191. 18-4 Standard Calibration Procedure 192. 18-5 Five-Point Calibration Procedure 193. 18-6 Process Calibrators 194. 18-7 Tuning the Controller 195. 18-8 Trial-and-Error Tuning Method 196. 18-9 Ziegler-Nichols Continuous-Cycling Method 197. 18-10 Ziegler-Nichols Reaction-Curve Tuning Method 198. 18-11 Controller Autotuning 199. Problems 200. Section 6: Detection Sensors 201. Ch 19: Industrial Detection Sensors and Interfacing
- 10. 202. Introduction 203. 19-1 Limit Switches 204. 19-2 Proximity Detectors 205. 19-3 Inductive Proximity Switches 206. 19-4 Capacitive Proximity Switches 207. 19-5 Hall-Effect Sensor 208. 19-6 Photoelectric Sensors 209. 19-7 Methods of Detection 210. 19-8 Photoelectric Sensor Adjustable Controls 211. 19-9 Photoelectric Package Styles 212. 19-10 Operating Specifications 213. 19-11 Ultrasonic Sensors 214. 19-12 Sensor Interfacing 215. Problems 216. Ch 20: Industrial Wireless Technologies 217. Introduction 218. 20-1 Wireless Architecture 219. 20-2 Wireless Signals 220. 20-3 Wireless Topologies 221. 20-4 Self-Organizing Networks 222. 20-5 Wireless Technologies 223. 20-6 Radio Frequencies 224. 20-7 Characteristics of the Radio Path 225. 20-8 Power Management of Field Devices 226. 20-9 Security 227. 20-10 Wireless Standards 228. Problems 229. Section 7: Programmable Controllers 230. Ch 21: Introduction to Programmable Controllers 231. Introduction to PLC Functions 232. 21-1 Industrial Motor Control Circuits 233. 21-2 Relay Ladder Logic Circuits 234. 21-3 Building a Ladder Diagram 235. 21-4 Motor Starter Control Circuits 236. Introduction to PLC Components 237. 21-5 Rack Assembly 238. 21-6 Power Supply 239. 21-7 PLC Programming Units 240. 21-8 Input/Output Sections 241. 21-9 Processor Unit 242. 21-10 Addressing 243. 21-11 Relationship of Data File Addresses to I/O Modules 244. Problems 245. Ch 22: Fundamental PLC Programming 246. Introduction 247. 22-1 PLC Program Execution
- 11. 248. 22-2 Ladder Diagram Programming Language 249. 22-3 Ladder Diagram Programming 250. 22-4 Relay Logic Instructions 251. 22-5 Timer Instructions 252. 22-6 Counter Instructions 253. 22-7 Data-Manipulation Instructions 254. 22-8 Arithmetic Operations 255. 22-9 Writing a Program 256. Problems 257. Ch 23: Advanced Programming, PLC Interfacing, and Troubleshooting 258. Introduction 259. 23-1 Jump Commands 260. 23-2 Data Manipulation 261. Programmable Controller Interfacing 262. 23-3 Discrete Input/Output Modules 263. 23-4 Troubleshooting I/O Interfaces 264. 23-5 Analog Input and Output Signals 265. 23-6 Special-Purpose Modules 266. 23-7 Troubleshooting Programmable Controllers 267. Problems 268. Section 8: Motion Control 269. Ch 24: Elements of Motion Control 270. Introduction 271. 24-1 Open-Loop and Closed-Loop Servo Systems 272. 24-2 Motion-Control Parameters 273. 24-3 Motion-Control Elements 274. 24-4 Terminology 275. 24-5 Operator Interface Block 276. 24-6 Controller Block 277. 24-7 Amplifier Block 278. 24-8 Actuator Block 279. 24-9 Feedback Transducer Block 280. Problems 281. Ch 25: Motion-Control Feedback Devices 282. Introduction 283. 25-1 Angular Velocity Feedback Devices 284. 25-2 Angular Displacement Feedback Devices 285. 25-3 Linear Displacement Feedback Devices 286. Problems 287. Ch 26: Fundamentals of Servomechanisms 288. Introduction 289. 26-1 Closed-Loop Velocity Servo 290. 26-2 Bang-Bang Position Servo 291. 26-3 Proportional Position Servomechanisms 292. 26-4 Digital Position Control 293. 26-5 Characteristics of a Servomechanism
- 12. 294. 26-6 Designing a Position Servo 295. 26-7 Digital Controller 296. 26-8 Tuning a Servomechanism 297. 26-9 Master-Slave Servosystem 298. Problems 299. Section 9: Industrial Networking 300. Ch 27: Industrial Networking 301. 27-1 Introduction 302. 27-2 Hierarchy of Industrial Networks 303. 27-3 Network Topologies 304. 27-4 Data Flow Management 305. 27-5 Transmission Hardware 306. 27-6 Network Backbones 307. 27-7 Network Communication Standards 308. 27-8 Fieldbus Networks 309. Problems 310. Answers to Odd-Numbered Problems 311. Glossary 312. Index
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- 14. coincide with that of Newton. But this, as we shall presently see, is not the case; and this instance ought to serve to make us extremely cautious how we employ, in stating physical laws derived from experiment, language which involves any thing in the slightest degree theoretical, if we would present the laws themselves in a form which no future research shall modify or subvert. (279.) A third class of optical phenomena, which were likewise discovered while Newton was yet engaged in his optical researches, was that exhibited by doubly refracting crystals. In what the phenomenon of double refraction consists, we have already had occasion to explain. The fact itself was first noticed by Erasmus Bartolin in the crystal called Iceland spar; and was studied with attention by Huyghens, who ascertained its laws, and referred it with remarkable ingenuity and success to his theory of light, by the additional hypothesis of such a constitution of his ethereal medium within the crystal as should enable it to convey an impulse faster in one direction than another: as if, for example’s sake, we should suppose a sound conveyed through the air with different degrees of rapidity in a vertical and horizontal direction. (280.) Some remarkable facts accompanying the double refraction produced by Iceland spar, which Bartolin, Huyghens, and Newton, had observed, led the latter to conceive the singular idea that a ray of light after its emergence from such a crystal acquires sides, that is to say, distinct relations to surrounding space, which it carries with it through its whole subsequent course, and which give rise to all those curious and complicated phenomena which are now known under the name of the polarization of light. These results, however, appeared so extraordinary, and offered so little handle for further enquiry, that their examination dropped, as if by common consent; Newton himself resting content with urging strongly the apparent incompatibility of these properties with the Huyghenian doctrine, but without making any attempt to explain them by his own.
- 15. (281.) From the period of Newton’s optical discoveries to the commencement of the present century, no great accession to our knowledge of the nature of light was made, if we except one, which, from its invaluable practical application, must ever hold a prominent place in the annals both of art and science: we mean, the discovery of the principle of the achromatic telescope, which originated in a discussion between the celebrated geometer Euler, Klingenstierna, an eminent Swedish philosopher, and our own countryman, the admirable optician Dollond, on the occasion of certain abstract theoretical investigations of the former, which led him to speculate on its possibility, and which ultimately terminated in its complete and happy execution by the latter; a memorable case in science, though not a singular one, where the speculative geometer in his chamber, apart from the world, and existing among abstractions, has originated views of the noblest practical application. 49 (282.) The explanation which our knowledge of optical laws affords of the mechanism of the eye, and the process by which vision is performed, is as complete and satisfactory as that of hearing by the propagation of motion through the air. The camera obscura, invented by Baptista Porta in 1560, gave the first idea how the actual images of external objects might be conveyed into the eye, but it was not till after a considerable interval that Kepler, the immortal discoverer of those great laws which regulate the periods and motions of the planets, pointed out distinctly the offices performed by the several parts of the eye in the act of vision. From this to the invention of the telescope and microscope there would seem but a small step, but it is to accident rather than design that it is due; and its re-invention by Galileo, on a mere description of its effects, may serve, among a thousand similar instances, to show that inestimable practical applications lie open to us, if we can only once bring ourselves to conceive their possibility, a lesson which the invention of the achromatic telescope itself, as we have above related it, not less strongly exemplifies.
- 16. (283.) The little instrument with which Galileo’s splendid discoveries were made was hardly superior in power to an ordinary finder of the present day; but it was rapidly improved on, and in the hands of Huyghens attained to gigantic dimensions and very great power. It was to obviate the necessity of the enormous length required for these telescopes, and yet secure the same power, that Gregory and Newton devised the reflecting telescope, which has since become a much more powerful instrument than its original inventors probably ever contemplated. (284.) The telescope, as it exists at present, with the improvements in its structure and execution which modern artists have effected, must assuredly be ranked among the highest and most refined productions of human art; that in which man has been able to approximate most closely to the workmanship of nature, and which has conferred upon him, if not another sense, at least an exaltation of one already possessed by him that merits almost to be regarded as a new one. Nor does it appear yet to have reached its ultimate perfection, to which indeed it is difficult to assign any bounds, when we take into consideration the wonderful progress which workmanship of every kind is making, and the delicacy, far superior to that of former times, with which materials may now be wrought, as well as the ingenious inventions and combinations which every year is bringing forth for accomplishing the same ends by means hitherto unattempted. 50 (285.) After a long torpor, the knowledge of the properties of light began to make fresh progress about the end of the last century, advancing with an accelerated rapidity, which has continued unabated to the present time. The example was set by our late admirable and lamented countryman, Dr. Wollaston, who re- examined and verified the laws of double refraction in Iceland spar announced by Huyghens. Attention being thus drawn to the subject, the geometry of Laplace soon found a means of explaining at least one portion of the mystery of this singular phenomenon, by the Newtonian theory of light, applied under certain supposed
- 17. conditions; and the reasoning which led him to the result (at that time quite unexpected), may justly be regarded as one of his happiest efforts. The prosecution of the subject, which had now acquired a high degree of interest, was encouraged by the offer of a prize on the part of the French Academy of Sciences; and it was in a memoir which received this honourable reward on that occasion, in 1810, that Malus, a retired officer of engineers in the French army, announced the great discovery of the polarization of light by ordinary reflection at the surface of a transparent body. (286.) Malus found that when a beam of light is reflected from the surface of such a body at a certain angle, it acquires precisely the same singular property which is impressed upon it in the act of double refraction, and which Newton had before expressed by saying that it possessed sides. This was the first circumstance which pointed out a connection between that hitherto mysterious phenomenon and any of the ordinary modifications of light; and it proved ultimately the means of bringing the whole within the limits, if not of a complete explanation, at least of a highly plausible theoretical representation. So true is, in science, the remark of Bacon, that no natural phenomenon can be adequately studied in itself alone, but, to be understood, must be considered as it stands connected with all nature. (287.) The new class of phenomena thus disclosed were immediately studied with diligence and success, both abroad by Malus and Arago, and at home by our countryman Dr. Brewster, and their laws investigated with a care proportioned to their importance; when another and apparently still more extraordinary class of phenomena presented itself in the production of the most vivid and beautiful colours (every way resembling those observed by Newton in thin films of air or liquids, only infinitely more developed and striking,) in certain transparent crystallized substances, when divided into flat plates in particular directions, and exposed in a beam of polarized light. The attentive examination of these colours by Wollaston, Biot, and Arago, but more especially by Brewster, speedily led to the disclosure of a series of optical phenomena so various, so
- 18. brilliant, and evidently so closely connected with the most important points relating to the intimate structure of crystallized bodies, as to excite the highest interest,—that sort of interest which is raised when we feel we are on the eve of some extraordinary discovery, and expect every moment that some leading fact will turn up, which will throw light on all that appears obscure, and reduce into order all that seems anomalous. (288.) This expectation was not disappointed. So long before the time we are speaking of as the first year of the present century, our illustrious countryman, the late Dr. Thomas Young, had established a principle in optics, which, regarded as a physical law, has hardly its equal for beauty, simplicity, and extent of application, in the whole circle of science. Considering the manner in which the vibrations of two musical sounds arriving at once at the ear affect the sense with an impression of sound or silence according as they conspire or oppose each other’s effects, he was led to the idea that the same ought to hold good with light as with sound, if the theory which makes light analogous to sound be the true one; and that, therefore, two rays of light, setting off from the same origin, at the same instant, and arriving at the same place by different routes, ought to strengthen or wholly or partially destroy each other’s effects according to the difference in length of the routes described by them. That two lights should in any circumstances combine to produce darkness may be considered strange, but is literally true; and it had even been noticed long ago as a singular and unaccountable fact by Grimaldi, in his experiments on the inflection of light. The experimental means by which Dr. Young confirmed this principle, which is known in optics by the name of the interference of the rays of light, were as simple and satisfactory as the principle itself is beautiful; but the verifications of it, drawn from the explanation it affords of phenomena apparently the most remote, are still more so. Newton’s colours of thin films were the first phenomena to which its author applied it with full success. Its next remarkable application was to those of diffraction, of which, in the hands of M. Fresnel, a late eminent French geometer, it also
- 19. furnished a complete explanation, and that, too, in cases to which Newton’s hypothesis could not apparently be made to apply, and through a complication of circumstances which might afford a very severe test of any hypothesis. (289.) A simple and beautiful experiment on the interferences of polarized light due to Fresnel and Arago enabled them to bring Dr. Young’s law to bear on the colours produced by crystallized plates in a polarized beam, and by so doing afforded a key to all the intricacies of these magnificent but complex phenomena. Nothing now was wanting to a rational theory of double refraction but to frame an hypothesis of some mode in which light might be conceived to be propagated through the elastic medium supposed to convey it in such a way as not to be contradictory to any of the facts, nor to the general laws of dynamics. This essential idea, without which every thing that had been before done would have been incomplete, was also furnished by Dr. Young, who, with a sagacity which would have done honour to Newton himself, had declared, that to accommodate the doctrine of Huyghens to the phenomena of polarized light it is necessary to conceive the mode of propagation of a luminous impulse through the ether, differently from that of a sonorous one through the air. In the latter, the particles of the air advance and recede; in the former, those of the ether must be supposed to tremble laterally. (290.) Taking this as the groundwork of his reasoning, Fresnel succeeded in erecting on it a theory of polarization and double refraction, so happy in its adaptation to facts, and in the coincidence with experience of results deduced from it by the most intricate analysis, that it is difficult to conceive it unfounded. If it be so, it is at least the most curiously artificial system that science has yet witnessed; and whether it be so or not, so long as it serves to group together in one comprehensive point of view a mass of facts almost infinite in number and variety, to reason from one to another, and to establish analogies and relations between them; on whatever hypothesis it may be founded, or whatever arbitrary assumptions it may make respecting structures and modes of action, it can never
- 20. be regarded as other than a most real and important accession to our knowledge. (291.) Still, it is by no means impossible that the Newtonian theory of light, if cultivated with equal diligence with the Huyghenian, might lead to an equally plausible explanation of phenomena now regarded as beyond its reach. M. Biot is the author of the hypothesis we have already mentioned of a rotatory motion of the particles of light about their axes. He has employed it only for a very limited purpose; but it might doubtless be carried much farther; and by admitting only the regular emission of the luminous particles at equal intervals of time, and in similar states of motion from the shining body, which does not seem a very forced supposition, all the phenomena of interference at least would be readily enough explained without the admission of an ether. (292.) The optical examination of crystallized substances affords one among many fine examples of the elucidation which every branch of science is capable of affording to every other. The indefatigable researches of Dr. Brewster and others have shown that the phenomena exhibited by polarized light in its transmission through crystals afford a certain indication of the most important points relating to the structure of the crystals themselves, and thus become most valuable characters by which to recognise their internal constitution. It was Newton who first showed of what importance as a physical character,—as the indication of other properties,—the action of a body on light might become; but the characters afforded by the use of polarized light as an instrument of experimental enquiry are so marked and intimate, that they may almost be said to have furnished us with a kind of intellectual sense, by which we are enabled to scrutinize the internal arrangement of those wonderful structures which Nature builds up by her refined and invisible architecture, with a delicacy eluding our conception, yet with a symmetry and beauty which we are never weary of admiring. In this point of view the science of optics has rendered to mineralogy and crystallography services not less important than to astronomy by the invention of the telescope, or to natural history by
- 21. that of the microscope; while the relations which have been discovered to exist between the optical properties of bodies and their crystalline forms, and even their chemical habitudes, have afforded numerous and beautiful instances of general laws concluded from laborious and painful induction, and curiously exemplifying the simplicity of nature as it emerges slowly from an entangled mass of particulars in which, at first, neither order nor connection can be traced.
- 22. CHAP. III. OF COSMICAL PHENOMENA. Astronomy and Celestial Mechanics. (293.) Astronomy, as has been observed in the former part of this discourse, as a science of observation, had made considerable progress among the ancients: indeed, it was the only branch of physical science which could be regarded as having been cultivated by them with any degree of assiduity or real success. The Chaldean and Egyptian records had furnished materials from which the motions of the sun and moon could be calculated with sufficient exactness for the prediction of eclipses; and some remarkable cycles, or periods of years in which the lunar eclipses return in very nearly the same order, had been ascertained by observation. Considering the extreme imperfection of their means of measuring time and space, this was, perhaps, as much as could have been expected at that early period, and it was followed up for a while in a philosophical spirit of just speculation, which, if continued, could hardly have failed to lead to sound and important conclusions. (294.) Unfortunately, however, the philosophy of Aristotle laid it down as a principle, that the celestial motions were regulated by laws proper to themselves, and bearing no affinity to those which prevail on earth. By thus drawing a broad and impassable line of separation between celestial and terrestrial mechanics, it placed the
- 23. former altogether out of the pale of experimental research, while it at the same time impeded the progress of the latter by the assumption of principles respecting natural and unnatural motions, hastily adopted from the most superficial and cursory remark, undeserving even the name of observation. Astronomy, therefore, continued for ages a science of mere record, in which theory had no part, except in so far as it attempted to conciliate the inequalities of the celestial motions with that assumed law of uniform circular revolution which was alone considered consistent with the perfection of the heavenly mechanism. Hence arose an unwieldy, if not self- contradictory, mass of hypothetical motions of sun, moon, and planets, in circles, whose centres were carried round in other circles, and these again in others without end,—“cycle on epicycle, orb on orb,”—till at length, as observation grew more exact, and fresh epicycles were continually added, the absurdity of so cumbrous a mechanism became too palpable to be borne. Doubts were expressed, to which the sarcasm of a monarch 51 gave a currency they might not have obtained in a period when men scarcely dared trust themselves to think; and at length Copernicus, promulgating his own, or reviving the Pythagorean doctrine, which places the sun in the centre of our system, gave to astronomy a simplicity which, contrasted with the complication of the preceding views, at once commanded assent. (295.) An elegant writer 52 , whom we have before had occasion to quote, has briefly and neatly accounted for the confused notions which so long prevailed respecting the constitution of our system, and the difficulty experienced in acquiring a true notion of the disposition of its parts. “We see it,” he observes, “not in plan, but in section.” The reason of this is, that our point of observation lies in its general plane, but the notion we aim at forming of it is not that of its section, but of its plan. This is as if we should attempt to read a book, or make out the countries on a map, with the eye on a level with the paper. We can only judge directly of the distances of objects by their sizes, or rather of their change of distance by their change
- 24. of size; neither have we any means of ascertaining, otherwise than indirectly, even their positions, one among the other, from their apparent places as seen by us. Now, the variations in apparent size of the sun and moon are too small to admit of exact measure without the use of the telescope, and the bodies of the planets cannot even be distinguished as having any distinct size with the naked eye. (296.) The Copernican system once admitted, however, this difficulty of conception, at least, is effectually got over, and it becomes a mere problem of geometry and calculation to determine, from the observed places of a planet, its real orbit about the sun, and the other circumstances of its motion. This Kepler accomplished for the orbit of Mars, which he ascertained to be an ellipse having the sun in one of its foci; and the same law, being extended by inductive analogy to all the planets, was found to be verified in the case of each. This with the other remarkable laws which are usually cited in physical astronomy by the name of Kepler’s laws, constitute undoubtedly the most important and beautiful system of geometrical relations which have ever been discovered by a mere inductive process, independent of any consideration of a theoretical kind. They comprise within them a compendium of the motions of all the planets, and enable us to assign their places in their orbits at any instant of time past or to come (disregarding their mutual perturbations), provided certain purely geometrical problems can be numerically resolved. (297.) It was not, however, till long after Kepler’s time that the real importance of these laws could be felt. Regarded in themselves, they offered, it is true, a fine example of regular and harmonious disposition in the greatest of all the works of creation, and a striking contrast to the cumbersome mechanism of the cycles and epicycles which preceded them; but there their utility seemed to terminate, and, indeed, Kepler was reproached, and not without a semblance of reason, with having rendered the actual calculation of the places of the planets more difficult than before, the resources of geometry
- 25. being then inadequate to resolve the problems to which the strict application of his laws gave rise. (298.) The first result of the invention of the telescope and its application to astronomical purposes, by Galileo, was the discovery of Jupiter’s disc and satellites,—of a system offering a beautiful miniature of that greater one of which it forms a portion, and presenting to the eye of sense, at a single glance, that disposition of parts which in the planetary system itself is discerned only by the eye of reason and imagination (see 195.). Kepler had the satisfaction of seeing it ascertained, that the law which he had discovered to connect the times of revolution of the planets with their distances from the sun, holds good also when applied to the periods of circulation of these little attendants round the centre of their principal; thus demonstrating it to be something more than a mere empirical rule, and to depend on the intimate nature of planetary motion itself. (299.) It had been objected to the doctrine of Copernicus, that, were it true, Venus should appear sometimes horned like the moon. To this he answered by admitting the conclusion, and averring that, should we ever be able to see its actual shape, it would appear so. It is easy to imagine with what force the application would strike every mind when the telescope confirmed this prediction, and showed the planet just as both the philosopher and his objectors had agreed it ought to appear. The history of science affords perhaps only one instance analogous to this. When Dr. Hutton expounded his theory of the consolidation of rocks by the application of heat, at a great depth below the bed of the ocean, and especially of that of marble by actual fusion; it was objected that, whatever might be the case with others, with calcareous or marble rocks, at least, it was impossible to grant such a cause of consolidation, since heat decomposes their substance and converts it into quicklime, by driving off the carbonic acid, and leaving a substance perfectly infusible, and incapable even of agglutination by heat. To this he replied, that the pressure under which the heat was applied would prevent the escape of the carbonic acid; and that being retained, it
- 26. might be expected to give that fusibility to the compound which the simple quicklime wanted. The next generation saw this anticipation converted into an observed fact, and verified by the direct experiments of Sir James Hall, who actually succeeded in melting marble, by retaining its carbonic acid under violent pressure. (300.) Kepler, among a number of vague and even wild speculations on the causes of the motions whose laws he had developed so beautifully and with so much patient labour, had obtained a glimpse of the general law of the inertia of matter, as applicable to the great masses of the heavenly bodies as well as to those with which we are conversant on the earth. After Kepler, Galileo, while he gave the finishing blow to the Aristotelian dogmas which erected a barrier between the laws of celestial and terrestrial motion, by his powerful argument and caustic ridicule, contributed, by his investigations of the laws of falling bodies and the motions of projectiles, to lay the foundation of a true system of dynamics, by which motions could be determined from a knowledge of the forces producing them, and forces from the motions they produce. Hooke went yet farther, and obtained a view so distinct of the mode in which the planets might be retained in their orbits by the sun’s attraction, that, had his mathematical attainments been equal to his philosophical acumen, and his scientific pursuits been less various and desultory, it can hardly be doubted that he would have arrived at a knowledge of the law of gravitation. (301.) But every thing which had been done towards this great end, before Newton, could only be regarded as smoothing some first obstacles, and preparing a state of knowledge, in which powers like his could be effectually exerted. His wonderful combination of mathematical skill with physical research enabled him to invent, at pleasure, new and unheard-of methods of investigating the effects of those causes which his clear and penetrating mind detected in operation. Whatever department of science he touched, he may be said to have formed afresh. Ascending by a series of close- compacted inductive arguments to the highest axioms of dynamical science, he succeeded in applying them to the complete explanation
- 27. of all the great astronomical phenomena, and many of the minuter and more enigmatical ones. In doing this, he had every thing to create: the mathematics of his age proved totally inadequate to grapple with the numerous difficulties which were to be overcome; but this, so far from discouraging him, served only to afford new opportunities for the exertion of his genius, which, in the invention of the method of fluxions, or, as it is now more generally called, the differential calculus, has supplied a means of discovery, bearing the same proportion to the methods previously in use, that the steam- engine does to the mechanical powers employed before its invention. Of the optical discoveries of Newton we have already spoken; and if the magnitude of the objects of his astronomical discoveries excite our admiration of the mental powers which could so familiarly grasp them, the minuteness of the researches into which he there set the first example of entering, is no less calculated to produce a corresponding impression. Whichever way we turn our view, we find ourselves compelled to bow before his genius, and to assign to the name of Newton a place in our veneration which belongs to no other in the annals of science. His era marks the accomplished maturity of the human reason as applied to such objects. Every thing which went before might be more properly compared to the first imperfect attempts of childhood, or the essays of inexpert, though promising, adolescence. Whatever has been since performed, however great in itself, and worthy of so splendid and auspicious a beginning, has never, in point of intellectual effort, surpassed that astonishing one which produced the Principia. (302.) In this great work, Newton shows all the celestial motions known in his time to be consequences of the simple law, that every particle of matter attracts every other particle in the universe with a force proportional to the product of their masses directly, and the square of their mutual distance inversely, and is itself attracted with an equal force. Setting out from this, he explains how an attraction arises between the great spherical masses of which our system consists, regulated by a law precisely similar in its expression; how the elliptic motions of planets about the sun, and of satellites about
- 28. their primaries, according to the exact rules inductively arrived at by Kepler, result as necessary consequences from the same general law of force; and how the orbits of comets themselves are only particular cases of planetary movements. Thence proceeding to applications of greater difficulty, he explains how the perplexing inequalities of the moon’s motion result from the sun’s disturbing action; how tides arise from the unequal attraction of the sun as well as of the moon on the earth, and the ocean which surrounds it; and, lastly, how the precession of the equinoxes is a necessary consequence of the very same law. (303.) The immediate successors of Newton found full occupation in verifying his discoveries, and in extending and improving the mathematical methods which it had now become manifest were to prove the keys to an inexhaustible treasure of knowledge. The simultaneous but independent discovery of a method of mathematical investigation in every respect similar to that of Newton, by Leibnitz, while it created a degree of national jealousy which can now only be regretted, had the effect of stimulating the continental geometers to its cultivation, and impressing on it a character more entirely independent of the ancient geometry, to which Newton was peculiarly attached. It was fortunate for science that it did so; for it was speedily found that (with one fine exception on the part of our countryman Maclaurin, followed up, after a long interval, by the late Professor Robison of Edinburgh, with equal elegance,) the geometry of Newton was like the bow of Ulysses, which none but its master could bend; and that, to render his methods available beyond the points to which he himself carried them, it was necessary to strip them of every vestige of that antique dress in which he had delighted to clothe them. This, however, the countrymen of Newton were very unwilling to do; and they paid the penalty in finding themselves condemned to the situation of lookers on, while their continental neighbours both in Germany and France were pushing forward in the career of mathematico-physical discovery with emulous rapidity.
- 29. (304.) The legacy of research which Newton may be said to have left to his successors was truly immense. To pursue, through all its intricacies, the consequences of the law of gravitation; to account for all the inequalities of the planetary movements, and the infinitely more complicated, and to us more important ones, of the moon; and to give, what Newton himself certainly never entertained a conception of, a demonstration of the stability and permanence of the system, under all the accumulating influence of its internal perturbations; this labour, and this triumph, were reserved for the succeeding age, and have been shared in succession by Clairaut, D’Alembert, Euler, Lagrange and Laplace. Yet so extensive is the subject, and so difficult and intricate the purely mathematical enquiries to which it leads, that another century may yet be required to go through with the task. The recent discoveries of astronomers have supplied matter for investigation, to the geometers of this and the next generation, of a difficulty far surpassing any thing that had before occurred. Five primary planets have been added to our system; four of them since the commencement of the present century, and these, singularly deviating from the general analogy of the others, and offering cases of difficulty in theory, which no one had before contemplated. Yet even the intricate questions to which these bodies have given rise seem likely to be surpassed by those which have come into view, with the discovery of several comets revolving in elliptic orbits, like the planets, round the sun, in very moderate periods. But the resources of modern geometry seem, so far from being exhausted, to increase with the difficulties they have to encounter, and already, among the successors of Lagrange and Laplace, the present generation has to enumerate a powerful array of names, which promise to render it not less celebrated in the annals of physico-mathematical research than that which has just passed away. (305.) Meanwhile the positions, figures, and dimensions of all the planetary orbits, are now well known, and their variations from century to century in great measure determined; and it has been generally demonstrated, that all the changes which the mutual
- 30. actions of the planets on each other can produce in the course of indefinite ages, are periodical, that is to say, increasing to a certain extent (and that never a very great one), and then again decreasing; so that the system can never be destroyed or subverted by the mutual action of its parts, but keeps constantly oscillating, as it were, round a certain mean state, from which it can never deviate to any ruinous extent. In particular the researches of Laplace, Lagrange, and Poisson, have shown the ultimate invariability of the mean distance of each planet from the sun, and consequently of its periodic time. Relying on these grand discoveries, we are enabled to look forward, from the point of time which we now occupy, many thousands of years into futurity, and predict the state of our system without fear of material error, but such as may arise from causes whose existence at present we have no reason to suppose, or from interference which we have no right to anticipate. (306.) A correct enumeration and description of the fixed stars in catalogues, and an exact knowledge of their position, supply the only effectual means we can have of ascertaining what changes they are liable to, and what motions, too slow to deprive them of their usual epithet, fixed, yet sufficient to produce a sensible change in the lapse of ages, may exist among them. Previous to the invention of the compass, they served as guides to the navigator by night; but for this purpose, a very moderate knowledge of a few of the principal ones sufficed. Hipparchus was the first astronomer, who, excited by the appearance of a new star, conceived the idea of forming a catalogue of the stars, with a view to its use as an astronomical record, “by which,” says Pliny, “posterity will be able to discover, not only whether they are born and die, but also whether they change their places, and whether they increase or decrease.” His catalogue, containing more than 1000 stars, was constructed about 128 years before Christ. It was in the course of the laborious discussion of his own and former observations of them, undertaken with a view to the formation of this catalogue, that he first recognised the fact of that slow, general advance of all the stars eastward, when compared with the place of the equinox, which is
- 31. known under the name of the precession of the equinoxes, and which Newton succeeded in referring to a motion in the earth’s axis, produced by the attraction of the sun and moon. (307.) Since Hipparchus, at various periods in the history of astronomy, catalogues of stars have been formed, among which that of Ulugh Begh, comprising about 1000 stars, constructed in 1437, is remarkable as the production of a sovereign prince, working personally in conjunction with his astronomers; and that of Tycho Brahe, containing 777 stars, constructed in 1600, as having originated in a phenomenon similar to that which drew the attention of Hipparchus. In more recent times, astronomers provided with the finest instruments their respective eras could supply, and established in observatories, munificently endowed by the sovereigns and governments of different European nations, have vied and are still vying with each other, in extending the number of registered stars, and giving the utmost possible degree of accuracy to the determination of their places. Among these, it would be ungrateful not to claim especial notice for the superb series of observations which, under a succession of indefatigable and meritorious astronomers, has, for a very long period, continued to emanate from our own national observatory of Greenwich. (308.) The distance of the fixed stars is so immense, that every attempt to assign a limit, within which it must fall, has hitherto failed. The enquiries of astronomers of all ages have been directed to ascertain this distance, by taking the dimensions of our own particular system of sun and planets, or of the earth itself, as the unit of a scale on which it might be measured. But although many have imagined that their observations afforded grounds for the decision of this interesting point, it has uniformly happened either that the phenomena on which they relied have proved to be referable to other causes not previously known, and which the superior accuracy of their researches has for the first time brought to light; or to errors arising from instrumental imperfections and unavoidable defects of the observations themselves.
- 32. (309.) The only indication we can expect to obtain of the actual distance of a star, would consist in an annual change in its apparent place corresponding to the motion of the earth round the sun, called its annual parallax, and which is nothing more than the measure of the apparent size of the earth’s orbit as seen from the star. Many observers have thought they have detected a measurable amount of this parallax; but as astronomical instruments have advanced in perfection, the quantity which they have successively assigned to it has been continually reduced within narrower and narrower limits, and has invariably been commensurate with the errors to which the instruments used might fairly be considered liable. The conclusion this strongly presses on us is, that it is really a quantity too small to admit of distinct measurement in the present state of our means for that purpose; and that, therefore, the distance of the stars must be a magnitude of such an order as the imagination almost shrinks from contemplating. But this increase in our scale of dimension calls for a corresponding enlargement of conception in all other respects. The same reasoning which places the stars at such immeasurable remoteness, exalts them at the same time into glorious bodies, similar to, and even far surpassing, our own sun, the centres perhaps of other planetary systems, or fulfilling purposes of which we can have no idea, from any analogy in what passes immediately around us. (310.) The comparison of catalogues, published at different periods, has given occasion to many curious remarks, respecting changes both of place and brightness among the stars, to the discovery of variable ones which lose and recover their lustre periodically, and to that of the disappearance of several from the heavens so completely as to have left no vestige discernible even by powerful telescopes. In proportion as the construction of astronomical and optical instruments has gone on improving, our knowledge of the contents of the heavens has undergone a corresponding extension, and, at the same time, attained a degree of precision which could not have been anticipated in former ages. The places of all the principal stars in the northern hemisphere, and
- 33. of a great many in the southern, are now known to a degree of nicety which must infallibly detect any real motions that may exist among them, and has in fact done so, in a great many instances, some of them very remarkable ones. (311.) It is only since a comparatively recent date, however, that any great attention has been bestowed on the smaller stars, among which there can be no doubt of the most interesting and instructive phenomena being sooner or later brought to light. The minute examination of them with powerful telescopes, and with delicate instruments for the determination of their places, has, indeed, already produced immense catalogues and masses of observations, in which thousands of stars invisible to the naked eye are registered; and has led to the discovery of innumerable important and curious facts, and disclosed the existence of whole classes of celestial objects, of a nature so wonderful as to give room for unbounded speculation on the extent and construction of the universe. (312.) Among these, perhaps the most remarkable are the revolving double stars, or stars which, to the naked eye or to inferior telescopes, appear single; but, if examined with high magnifying powers, are found to consist of two individuals placed almost close together, and which, when carefully watched, are (many of them) found to revolve in regular elliptic orbits about each other; and so far as we have yet been able to ascertain, to obey the same laws which regulate the planetary movements. There is nothing calculated to give a grander idea of the scale on which the sidereal heavens are constructed than these beautiful systems. When we see such magnificent bodies united in pairs, undoubtedly by the same bond of mutual gravitation which holds together our own system, and sweeping over their enormous orbits, in periods comprehending many centuries, we admit at once that they must be accomplishing ends in creation which will remain for ever unknown to man; and that we have here attained a point in science where the human intellect is compelled to acknowledge its weakness, and to feel that no conception the wildest imagination can form will bear the least comparison with the intrinsic greatness of the subject.
- 34. Geology. (313.) The researches of physical astronomy are confessedly incompetent to carry us back to the origin of our system, or to a period when its state was, in any great essential, different from what it is at present. So far as the causes now in action go, and so far as our calculations will enable us to estimate their effects, we are equally unable to perceive in the general phenomena of the planetary system either the evidence of a beginning, or the prospect of an end. Geometers, as already stated, have demonstrated that, in the midst of all the fluctuations which can possibly take place in the elements of the orbits of the planets, by reason of their mutual attraction, the general balance of the parts of the system will always be preserved, and every departure from a mean state periodically compensated. But neither the researches of the physical astronomer, nor those of the geologist, give us any ground for regarding our system, or the globe we inhabit, as of eternal duration. On the contrary, there are circumstances in the physical constitution of our own planet which at least obscurely point to an origin and a formation, however remote, since it has been found that the figure of the earth is not globular but elliptical, and that its attraction is such as requires us to admit the interior to be more dense than the exterior, and the density to increase with some degree of regularity from the surface towards the centre, and that, in layers arranged elliptically round the centre, circumstances which could scarcely happen without some such successive deposition of materials as would enable pressure to be propagated with a certain degree of freedom from one part of the mass to another, even if we should hesitate to admit a state of primitive fluidity. (314.) But from such indications nothing distinct can be concluded; and if we would speculate to any purpose on a former state of our globe and on the succession of events which from time to time may have changed the condition and form of its surface, we must confine our views within limits far more restricted, and to subjects much more within the reach of our capacity, than either the
- 35. creation of the world or its assumption of its present figure. These, indeed, were favourite speculations with a race of geologists now extinct; but the science itself has undergone a total change of character, even within the last half century, and is brought, at length, effectually within the list of the inductive sciences. Geologists now no longer bewilder their imaginations with wild theories of the formation of the globe from chaos, or its passage through a series of hypothetical transformations, but rather aim at a careful and accurate examination of the records of its former state, which they find indelibly impressed on the great features of its actual surface, and to the evidences of former life and habitation which organised remains imbedded and preserved in its strata indisputably afford. (315.) Records of this kind are neither few nor vague; and though the obsoleteness of their language when we endeavour to interpret it too minutely, may, and no doubt often does, lead to misapprehension, still its general meaning is, on the whole, unequivocal and satisfactory. Such records teach us, in terms too plain to be misunderstood, that the whole or nearly the whole of our present lands and continents were formerly at the bottom of the sea, where they received deposits of materials from the wearing and degradation of other lands not now existing, and furnished receptacles for the remains of marine animals and plants inhabiting the ocean above them, as well as for similar spoils of the land washed down into its bosom. (316.) These remains are occasionally brought to light; and their examination has afforded indubitable evidence of the former existence of a state of animated nature widely different from what now obtains on the globe, and of a period anterior to that in which it has been the habitation of man, or rather, indeed, of a series of periods, of unknown duration, in which both land and sea teemed with forms of animal and vegetable life, which have successively disappeared and given place to others, and these again to new races approximating gradually more and more nearly to those which now inhabit them, and at length comprehending species which have their counterparts existing.
- 36. (317.) These wrecks of a former state of nature, thus wonderfully preserved (like ancient medals and inscriptions in the ruins of an empire), afford a sort of rude chronology, by whose aid the successive depositions of the strata in which they are found may be marked out in epochs more or less definitely terminated, and each characterized by some peculiarity which enables us to recognise the deposits of any period, in whatever part of the world they may be found. And, so far as has been hitherto investigated, the order of succession in which these deposits have been formed appears to have been the same in every part of the globe. (318.) Many of the strata which thus bear evident marks of having been deposited at the bottom of the sea, and of course in a horizontal state, are now found in a position highly inclined to the horizon, and even occasionally vertical. And they often bear no less evident marks of violence, in their bending and fracture, the dislocation of parts which were once contiguous, and the existence of vast collections of broken fragments which afford every proof of great violence having been used in accomplishing some at least of the changes which have taken place. (319.) Besides the rocks which carry this internal evidence of submarine deposition, are many which exhibit no such proofs, but on the contrary hold out every appearance of owing their origin to volcanoes or to some other mode of igneous action; and in every part of the world, and among strata of all ages, there occur evidences of such action so abundant, and on such a scale, as to point out the volcano and the earthquake as agents which may have been instrumental in the production of those changes of level, and those violent dislocations which we perceive to have taken place. (320.) At all events, in accounting for those changes, geologists have no longer recourse, as formerly, to causes purely hypothetical, such as a shifting of the earth’s axis of rotation, bringing the sea to overflow the land, by a change in the place of the longer and shorter diameters of the spheroidal figure, nor to tides produced by the attraction of comets suddenly approaching very near the earth, nor
- 37. to any other fanciful and arbitrarily assumed hypotheses; but rather endeavour to confine themselves to a careful consideration of causes evidently in action at present, with a view to ascertain how far they, in the first instance, are capable of accounting for the facts observed, and thus legitimately bringing into view, as residual phenomena, those effects which cannot be so accounted for. When this shall have been in some measure accomplished, we shall be able to pronounce with greater security than at present respecting the necessity of admitting a long succession of tremendous and ravaging catastrophes and cataclysms,—epochs of terrific confusion and violence which many geologists (perhaps with justice) regard as indispensable to the explanation of the existing features of the world. We shall learn to distinguish between the effects which require for their production the sudden application of convulsive and fracturing efforts, and those, probably not less extensive, changes which may have been produced by forces equally or more powerful, but acting with less irregularity, and so distributed over time as to produce none of those interregnums of chaotic anarchy which we are apt to think (perhaps erroneously) great disfigurements of an order so beautiful and harmonious as that of nature. (321.) But to estimate justly the effects of causes now in action in geology is no easy task. There is no à priori or deductive process by which we can estimate the amount of the annual erosion, for instance, of a continent by the action of meteoric agents, rain, wind, frost, &c., nor the quantity of destruction produced on its coasts by the direct violence of the sea, nor the quantity of lava thrown up per annum by volcanoes over the whole surface of the earth, nor any similar effect. And to consult experience on all such points is a slow and painful process if rightly gone into, and a very fallible one if only partially executed. Much, then, at present must be left to opinion, and to that sort of clear-judging tact which sometimes anticipates experience; but this ought not to stand in the way of our making every possible effort to obtain accurate information on such points, by which alone geology can be rendered, if not an experimental science, at least a science of that kind of active observation which
- 38. forms the nearest approach to it, where actual experiment is impossible. (322.) Let us take, for example, the question, “What is the actual direction in which changes of relative level are taking place between the existing continents and seas?” If we consult partial experience, that is, all the information that we possess respecting ancient sea- marks, soundings, &c., we shall only find ourselves bewildered in a mass of conflicting, because imperfect, evidence. It is obvious that the only way to decide the point is to ascertain, by very precise and careful observations at proper stations on coasts, selected at points where there exist natural marks not liable to change in the course of at least a century, the true elevation of such marks above the mean level of the sea, and to multiply these stations sufficiently over the whole globe to be capable of affording real available knowledge. Now, this is not a very easy operation (considering the accuracy required); for the mean level of the sea can be determined by no single observation, any more than the mean height of the barometer at a given station, being affected both by periodical and accidental fluctuations due to tides, winds, waves, and currents. Yet if an instrument adapted for the purpose were constructed, and rendered easily attainable, and rules for its use carefully drawn up, there is little doubt we should soon (by the industry of observers scattered over the world) be in possession of a most valuable mass of information, which could not fail to afford a point of departure for the next generation, and furnish ground for the only kind of argument which ever can be conclusive on such subjects. (323.) Geology, in the magnitude and sublimity of the objects of which it treats, undoubtedly ranks, in the scale of the sciences, next to astronomy; like astronomy, too, its progress depends on the continual accumulation of observations carried on for ages. But, unlike astronomy, the observations on which it depends, when the whole extent of the subject to be explored is taken into consideration, can hardly yet be said to be more than commenced. Yet, to make up for this, there is another important difference, that while in the latter science it is impossible to recall the past or
- 39. anticipate the future, and observation is in consequence limited to a single fact in a single moment; in the former, the records of the past are always present;—they may be examined and re-examined as often as we please, and require nothing but diligence and judgment to put us in possession of their whole contents. Only a very small part of the surface of our globe has, however, been accurately examined in detail, and of that small portion we are only able to scratch the mere exterior, for so we must consider those excavations which we are apt to regard as searching the bowels of the earth; since the deepest mines which have been sunk penetrate to a depth hardly surpassing the ten thousandth part of the distance between its surface and its centre. Of course inductions founded on such limited examination can only be regarded as provisional, except in those remarkable cases where the same great formations in the same order have been recognised in very distant quarters, and without exception. This, however, cannot long be the case. The spirit with which the subject has been prosecuted for many years in our own country has been rewarded with so rich a harvest of surprising and unexpected discoveries, and has carried the investigation of our island into such detail, as to have excited a corresponding spirit among our continental neighbours; while the same zeal which animates our countrymen on their native shore accompanies them in their sojourns abroad, and has already begun to supply a fund of information respecting the geology of our Indian possessions, as well as of every other point where English intellect and research can penetrate. (324.) Nothing can be more desirable than that every possible facility and encouragement should be afforded for such researches, and indeed to the pursuits of the enlightened resident or traveller in every department of science, by the representatives of our national authority wherever our power extends. By these only can our knowledge of the actual state of the surface of the globe, and that of the animals and vegetables of the ancient continents and seas, be extended and perfected, while more complete information than we at present possess of the habits of those actually existing, and the
- 40. influence of changes of climate, food, and circumstances, on them, may be expected to render material assistance to our speculations respecting those which have become extinct.
- 41. CHAP. IV. OF THE EXAMINATION OF THE MATERIAL CONSTITUENTS OF THE WORLD. Mineralogy. (325.) The consideration of the history and structure of our globe, and the examination of the fossil contents of its strata, lead us naturally to consider the materials of which it consists. The history of these materials, their properties as objects of philosophical enquiry, and their application to the useful arts and the embellishments of life, with the characters by which they can be certainly distinguished one from another, form the object of mineralogy, taken in its most extended sense. (326.) There is no branch of science which presents so many points of contact with other departments of physical research, and serves as a connecting link between so many distant points of philosophical speculation, as this. To the geologist, the chemist, the optician, the crystallographer, the physician, it offers especially the very elements of their knowledge, and a field for many of their most curious and important enquiries. Nor, with the exception of chemistry, is there any which has undergone more revolutions, or been exhibited in a greater variety of forms. To the ancients it could scarcely be said to be at all known, and up to a comparatively recent period, nothing could be more imperfect than its descriptions, or
- 42. more inartificial and unnatural than its classification. The more important minerals in the arts, indeed, those used for economical purposes and those from which metals were extracted, had a certain degree of attention paid to them, for the sake of their utility and commercial value, and the precious stones for that of ornament. But until their crystalline forms were attentively observed and shown to be determinate characters on which dependence could be placed, no mineralogist could give any correct account of the real distinction between one mineral and another. (327.) It was only, however, when chemical analysis had acquired a certain degree of precision and universal applicability that the importance of mineralogy as a science began to be recognized, and the connection between the external characters of a stone and its ingredient constituents brought into distinct notice. Among these characters, however, none were found to possess that eminent distinctness which the crystalline form offers; a character, in the highest degree geometrical, and affording, as might be naturally supposed, the strongest evidence of its necessary connection with the intimate constitution of the substance. The full importance of this character was, however, not felt until its connection with the texture or cleavage of a mineral was pointed out, and even then it required numerous and striking instances of the critical discernment of Haüy and other eminent mineralogists in predicting from the measurements of the angles of crystals which had been confounded together that differences would be found to exist in their chemical composition, all which proved fully justified in their result before the essential value of this character was acknowledged. This was no doubt in great measure owing to the high importance set by the German mineralogists on those external characters of touch, sight, weight, colour, and other sensible qualities, which are little susceptible, with the exception of weight, of exact determination, and which are subject to material variations in different specimens of the same mineral. By degrees, however, the necessity of ascribing great weight to a character so definite was admitted, especially when it was considered that the same step which pointed out the
- 43. intimate connection of external form with internal structure furnished the mineralogist with the means of reducing all the forms of which a mineral is susceptible under one general type, or primitive form, and afforded grounds for an elegant theoretical account of the assumption of definite figures ab initio. (328.) A simple and elegant invention of Dr. Wollaston, the reflecting goniometer, gave a fresh impulse to that view of mineralogy which makes the crystalline form the essential or leading character, by putting it in the power of every one, by the examination of even the smallest portion of a broken crystal, to ascertain and verify that essential character on which the identity of a mineral in the system of Haüy was made to depend. The application of so ready and exact a method speedily led to important results, and to a still nicer discrimination of mineral species than could before be attained; and the confirmation given to these results by chemical analysis stamped them with a scientific and decided character which they have retained ever since. (329.) Meanwhile the progress made in chemical analysis had led to the important conclusion that every chemical compound susceptible of assuming the solid state assumed with it a determinate crystalline form; and the progress of optical science had shown that the fundamental crystalline form, in the case at least of transparent bodies, drew with it a series of optical properties no less curious than important in relation to the affections of light in its passage through such substances. Thus, in every point of view, additional importance became added to this character; and the study of the crystalline forms of bodies in general assumed the form of a separate and independent branch of science, of which the geometrical forms of the mineral world constituted only a particular case. Mineralogy, however, as a branch of natural history, remains still distinct either from optics or crystallography. The mineralogist is content, and thinks he has performed his task, if not as a natural historian at least as a classifier and arranger, if he only gives such a characteristic description of a mineral as shall effectually distinguish it from every other, and shall enable any one who may encounter
- 44. such a body in any part of the world to impose on it its name, assign it a place in his system, and turn to his books for a further description of all that the chemist, the optician, the lapidary, or the artist, may require to know. Still this is no easy matter: the laborious researches of the most eminent mineralogists can hardly yet be said to have effectually accomplished it; and its difficulty may be appreciated by the small number of simple minerals, or minerals of perfectly definite and well-marked characters, which have been hitherto made out. Nor can this indeed be wondered at, when we consider that by far the greater portion of the rocks and stones which compose the external crust of the globe consists of nothing more than the accumulated detritus of older rocks, in which the fragments and powder of an infinite variety of substances are mingled together, in all sorts of varying proportions, and in such a way as to defy separation. Many of these rocks, however, so compounded, occur with sufficient frequency and uniformity of character to have acquired names and to have been usefully applied; indeed, in the latter respect, minerals of this description far surpass all the others. As objects of natural history, therefore, they are well worthy of attention, however difficult it may be to assign them a place in any artificial arrangement. (330.) This paucity of simple minerals, however, is probably rather apparent than real, and in proportion as the researches of the chemist and crystallographer shall be extended throughout nature, they will no doubt become much more numerous. Indeed, in the great laboratories of nature it can hardly be doubted that almost every kind of chemical process is going forwards, by which compounds of every description are continually forming. Accordingly, it is remarked, that the lavas and ejected scoriæ of volcanoes are receptacles in which mineral products previously unknown are constantly discovered, and that the primitive formations, as they are called in geology, which bear no marks of having been produced by the destruction of others, are also remarkable for the beauty and distinctness of character of their minerals.
- 45. (331.) The great difficulty which has been experienced in attempts to classify mineral substances by their chemical constituents has arisen from the observed presence, in some specimens of minerals bearing that general resemblance in other respects as well as agreement in form which would seem to entitle them to be considered as alike, of ingredients foreign to the usual composition of the species, and that occasionally in so large a proportion as to render it unjustifiable to refer their occurrence to accidental impurities. These cases, as well as some anomalies observed in the classification of minerals by their crystalline forms, which seemed to show that the same substance might occasionally appear under two distinct forms, as well as some remarkable coincidences between the forms of substances quite distinct from each other in a chemical point of view, have within a recent period given rise to a branch of the science of crystallography of a very curious and important nature. The isomorphism of certain groups of chemical elements has already afforded us an example illustrative of the manner in which inductions sometimes receive unexpected verifications (see 180.). The laws and relations thus brought to light are among the most curious and interesting parts of modern science, and seem likely in their further developement to afford ample scope for the exercise of chemical and mineralogical research. They have already afforded innumerable fine examples of that important step in science by which anomalies disappear, and occasional incongruities become reconciled under more general expressions of physical laws, and thus unite in affording support to those very views which they promised, when first observed, to overset. Nothing, indeed, can be more striking than to see the very ingredient which every previous chemist and mineralogist would agree to disregard and reject as a mere casual impurity brought forward and appealed to in support of a theory expressly directed to the object of rescuing science from the imputation of disregarding, under any circumstances, the plain results of direct experiment.
- 46. Chemistry. (332.) The laws which concern the intimate constitution of bodies, not as respects their structure or the manner in which their parts are put together, but as regards their materials or the ingredients of which those parts are composed, form the objects of chemistry. A solid body may be regarded as a fabric, more or less regularly and artificially constructed, in which the materials and the workmanship may be separately considered, and in which, though the latter be ruined and confounded by violence, the former remain unchanged in their nature, though differently arranged. In liquid or aërial bodies, too, though there prevails a less degree of difference in point of structure, and a greater facility of dispersion and dissipation, than in solids, yet an equal diversity of materials subsists, giving to them properties differing extremely from each other. (333.) The inherent activity of matter is proved not only by the production of motion by the mutual attractions and repulsions of distant or contiguous masses, but by the changes and apparent transformations which different substances undergo in their sensible qualities by mere mixture. If water be added to water, or salt to salt, the effect is an increase of quantity, but no change of quality. In this case, the mutual action of the particles is entirely mechanical. Again, if a blue powder and a yellow one, each perfectly dry, be mixed and well shaken together, a green powder will be produced; but this is a mere effect arising in the eye from the intimate mixture of the yellow and blue light separately and independently reflected from the minute particles of each; and the proof is had by examining the mixture with a microscope, when the yellow and blue grains will be seen separate and each quite unaltered. If the same experiment be tried with coloured liquids, which are susceptible of mixing without chemical action, a compound colour is likewise produced, but no examination with magnifiers is in that case sufficient to detect the ingredients; the reason obviously being, the excessive minuteness of the parts, and their perfect intermixture, produced by agitating two
- 47. liquids together. From the mixture of two powders, extreme patience would enable any one, by picking out with a magnifier grain after grain, to separate the ingredients. But when liquids are mixed, no mechanical separation is any longer practicable; the particles are so minute as to elude all search. Yet this does not hinder us from regarding such a compound as still a mere mixture, and its properties are accordingly intermediate between those of the liquids mixed. But this is far from being the case with all liquids. When a solution of potash, for example, and another of tartaric acid, each perfectly liquid, are mixed together in proper proportions, a great quantity of a solid saline substance falls to the bottom of the containing vessel, which is quite different from either potash or tartaric acid, and the liquid from which it subsided offers no indications by its taste or other sensible qualities of the ingredients mixed, but of something totally different from either. It is evident that this is a phenomenon widely different from that of mere mixture; there has taken place a great and radical change in the intimate nature of the ingredients, by which a new substance is produced which had no existence before. And it has been produced by the union of the ingredients presented to each other; for when examined it is found that nothing has been lost, the weight of the whole mixture being the sum of the weights mixed. Yet the potash and tartaric acid have disappeared entirely, and the weight of the new product is found to be exactly equal to that of the tartaric acid and potash employed, taken together, abating a small portion held in solution in the liquid, which may be obtained however by evaporation. They have therefore combined, and adhere to one another with a cohesive force sufficient to form a solid out of a liquid; a force which has thus been called into action by merely presenting them to each other in a state of solution. (334.) It is the business of chemistry to investigate these and similar changes, or the reverse of such changes, where a single substance is resolved into two or more others, having different properties from it, and from each other, and to enquire into all the circumstances which can influence them; and either determine,
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