CHAPTER XIX.

PLAIN RULES FOR RAILWAY SPECULATORS.

(142.) For some time after the completion of the Liverpool and Manchester railway, doubts were entertained of its ultimate success as a commercial speculation; and, even still, after several years' continuance, some persons are found, sceptical by temperament, who have not acquired full confidence in the permanency of its advantages. The possibility of sustaining a system of regular transport upon it, with the unheard of speed effected at the commencement of the undertaking, was, for a long period, questioned by a considerable portion even of the scientific world; and, after that possibility was established, by the regular performance of some years, the practicability of permanently profitable work, at that rate of speed, was still doubted by many, and altogether denied by some. The numerous difficulties to be encountered, and the enormous expense of locomotive power, have been fully admitted by the directors in their semi-annual reports. Persons interested in canals and other rival establishments, and others constitutionally doubtful of everything, attributed the dividends to the indirect proceedings of the managers, and asserted that when they appeared to be sharing their profit's, they, in reality, were sharing their capital. This delusion, however, could not long continue, and the payment of a steady semi-annual dividend of 4-1/2 per cent. since the opening of the railway, together with the commencement of a reserved fund of a considerable amount, with a premium of above 100 per cent. on the original shares, has brought conviction to understandings impenetrable to general reasoning; and the tide of opinion, which, for a time, had turned against railways, has now, by the usual reaction, set in so violently in their favour, that it becomes the duty of those who professionally devote themselves to such inquiries, to restrain and keep within moderate bounds the public ardour, rather than to stimulate it.

The projects for the construction of great lines of internal communication which have been announced would require, if realized, a very large amount of capital. Considering that the estimated capital is invariably less than the amount actually required, we shall not, perhaps, overrate the extent of the projected investments if we estimate them at fifty millions. The magnitude of this amount has created alarm in the minds of some persons, lest a change of investment so extensive should produce a serious commercial shock. It should, however, be considered that, even if all the projected undertakings should be ultimately carried into execution, a long period must elapse, perhaps not less than fifteen or twenty years, before they can be all completed: the capital will be required, not suddenly, but by small instalments, at distant intervals of time. Even if it were true, therefore, that, to sustain their enterprises, an equivalent amount of capital must be withdrawn from other investments, the transfer would lake place by such slow degrees as to create no serious inconvenience. But, in fact, it is not probable that any transfer of capital whatever will be necessary. Trade and manufacturers are at the present moment in a highly flourishing condition; and the annual accumulation of capital in the country is so great, that the difficulty will probably be, not to find capital to meet investments, but to find suitable investments for the increasing capital. In Manchester alone, it is said that the annual increment on capital is no less than three millions. In fifteen years, therefore, this mart alone would be sufficient to supply all the funds necessary for the completion of all the proposed railroads, without withdrawing capital from any other investment.

The facilities which these Joint Stock Companies offer for the investment of capital, even of the smallest amount, the temptations which the prospect of large profits hold out, and the low interest obtained on national stock of every description, have attracted a vast body of capitalists, small and great, who have subscribed to these undertakings with the real intention of investment. But, on the other hand, there is a very extensive body of speculators who engage in them upon a large scale, without the most distant intention, and, indeed, without the ability, of paying up the amount of their shares. The loss which the latter class of persons may sustain would, probably, excite little commiseration, were it not for the consequences which must result to the former, should a revolution take place, and the market be inundated with the shares of these gambling speculators, who buy only to sell again. Effects would be produced which must be ruinous to a large proportion of the _bonâ fide_ subscribers. It may, therefore, be attended with some advantage to persons who really intend to make permanent investments of this nature, to state, in succinct and intelligible terms, the principal circumstances on which the efficiency and economy of railroads depend, so as to enable them, in some measure, to form a probable conjecture of the prospective advantages which the various projects hold out. In doing this, we shall endeavour, as much as possible, to confine our statements to simple facts and results, which can neither be denied nor disputed, leaving, for the most part, the inferences to which they lead to be deduced from them by others.

It may be premised, that persons proposing to engage in any railroad speculation should obtain _first_ a table of _gradients_; that is, an account of all the acclivities upon the line from terminus to terminus, stating how many feet in a mile each incline rises or falls, and its length. _Secondly_, it would also be advantageous to have a statement of the lengths of the radii of the different _curves_ as well as the lengths of the curves themselves. _Thirdly_, an account of the actual intercourse which has taken place, for a given time, upon the turnpike road connecting the proposed termini, stating the number of coaches licensed, and the average number of passengers they carry; also as near an account of the transport of merchandise as may be obtained. The latter, however, is of less moment. An approximate estimate may be made of the intercourse in passengers, by allowing for each coach, upon each trip, half its licensed complement of load. _Fourthly_, the water communication by canal or otherwise between the places; and the amount of tonnage transported by it. With the information thus obtained, the following succinct maxims will be found useful:--

I.

No railroad can be profitably worked without a large intercourse of passengers. Goods, merchandise, agricultural produce, &c., ought to be regarded as of secondary importance.

II.

A probable estimate of the number of passengers to be expected upon a projected line of railroad may be made by increasing the average number of passengers for the last three years, by the common road, in a twofold proportion.

The average number of passengers daily between Liverpool and Manchester, before the formation of the railway, was about 450; the present average number is above 1300. A short railroad of about five miles is constructed between Dublin and Kingstown: on which the average number of passengers daily between those places has increased in nearly the same proportion.

III.

Passengers can be profitably transported by canal, at a speed not exceeding nine miles an hour, exclusive of delays at locks, at the rate of one penny per head per mile. The average fares charged upon the Manchester railway are at the rate of 1-84/100_d._ per head per mile, the average speed being twenty miles an hour.

To transport passengers at the rate of ten miles an hour on a railway, would cost very little less than the greater speed of twenty miles an hour, so that a railroad could not enter into competition on equal terms with a canal by equalising the speed.

The canal between Kendal and Preston measures 57 miles: passengers are transported upon it between these places at the average speed of a mile in 6-1/2 minutes, or 9-1/4 miles an hour nearly, exclusive of delays at locks. The fare charged is at the average rate of a penny a mile. There are eight locks, rising 9 feet each, and a tunnel 400 yards long, through which the boat is tracked by hand; the tunnel requires 5 minutes, and the locks from 25 to 28 minutes, in descending, and 45 to 48 minutes in ascending.

Similar boats are worked on the Forth and Clyde, and the Union canals in Scotland, and on the Paisley and Johnstone canal at nearly the same fares.

IV.

At the fare of 1-84/100_d._ per head per mile, the profit on the Manchester railroad is 100 per cent. on the disbursements for passengers.

V.

Goods can be profitably transported by canal at a lower tonnage than by railroads; the speed on the canal (for goods) being, however, but one-fifth of the speed on the railroad.

VI.

Goods are transported on the Liverpool and Manchester railroad at three-pence three farthings per ton per mile, with a profit of about 40 per cent. upon the disbursement, having the competition of a canal between its termini.

VII.

A long railroad can be worked with greater relative economy than a short one.

VIII.

Steam engines work with the greatest efficiency and economy, when the resistance they have to overcome is perfectly uniform and invariable.

IX.

The variation of resistance on railroads depends, first, on acclivities, secondly, on curves.

By curves are meant the changes of direction of the road to the right or to the left. The direction of a railroad cannot be changed suddenly by an angle, but must be effected gradually by a curve. Supposing the curve to be (as it generally is) the arc of a circle, the radius of the curve is the distance of the centre of the circle from the curve. This radius is an important element in the estimate of the road.

X.

The more nearly a railroad approaches to an absolute level, and perfect straightness, the more profitably will it be worked.

XI.

The total amount of mechanical power necessary to transfer a given load from one extremity of a railroad to another is a matter of easy and exact calculation, when the gradients and curves are known; and the merits of different lines may be compared together in this respect: but it is not the only test of their efficiency which must be applied.

XII.

A railroad having gradients exceeding seventeen feet in a mile will require more mechanical power to work it than it would were it level; and the more of these excessive gradients there are upon it, and the more steep they are, the greater will be this disadvantage.

XIII.

Although a railroad having no gradients exceeding seventeen feet in a mile does not require more mechanical power than a level, yet the mechanical power which it requires will not be so advantageously expended, and, therefore, it will not be so economical.

XIV.

A railroad which has gradients above thirty feet in a mile will require such gradients to be worked by assistant locomotive engines, which will be attended with a waste of power, and an increase of expenditure, more or less, according to the number and length of such gradients.

XV.

A very long inclined plane cannot be worked by an assistant locomotive without a wasteful expense. Gradients exceeding seventeen feet per mile must, therefore, be short.

XVI.

Gradients exceeding fifty feet in a mile cannot be profitably worked except by stationary engines and ropes, an expedient attended with so many objections as to be scarcely compatible with a large intercourse of passengers.

XVII.

Steep gradients, provided they descend from the extremities of a line, are admissible provided they be short.

It is evident that in this case the inclined planes will help at starting to put the trains in motion, at the time when, in general, there would be the greatest strain upon the moving power; and, in approaching the terminus, the momentum would be sufficient to carry the train to the top of the plane, if its length were not great, since it must, at all events, come to a stop at the extremity.

XVIII.

The effect of gradients in increasing the resistance during the ascent may be estimated by considering that a gradient of seventeen feet in a mile doubles the resistance of the level, thirty-four feet in a mile triples it, and eight and a half feet in a mile adds one half its amount, and so on.

XIX.

With the speed now attainable on railways, curves should be avoided with radii shorter than a mile. Expedients may diminish the resistance, but, through the negligence of engine drivers, they must always be attended with danger. Curves are not objectionable near the extremities of a line.

XX.

The worst position for a curve is the foot of an inclined plane, because of the velocity which the trains acquire in the descent, and the occasional impracticability of checking them.

XXI.

In proportion as the speed of locomotives is increased by the improvements they are likely to receive, the objections and dangers incident to curves will be increased.

XXII.

The difficulty which attends the use of long tunnels arises from the destruction of the vital air which is produced by the combustion in the furnaces of the engines. Tunnels on a level should, therefore, be from twenty-five to thirty feet high, and should be ventilated by shafts or other contrivances.

XXIII.

The transition from light to darkness, the sensation of humidity, and the change in summer from a warm atmosphere to a cold one, will always form an objection to long tunnels on lines of railroad intended for a large intercourse of passengers.

XXIV.

All the objections to a tunnel are aggravated when it happens to be upon an acclivity. The destruction of vital air in ascending it will be increased in exactly the same proportion as the moving power is increased. Thus, if it ascend 17 feet in a mile, the destruction of vital air will be twice as great as on a level; if it ascend 34 feet in a mile, it will be three times as great; 51 feet in a mile, four times as great, and so on.

XXV.

If by an overruling necessity a tunnel is constructed on an acclivity, its magnitude and means of ventilation should be greater than on a level, in the same proportion as the resistance produced by the acclivity is greater than the resistance upon a level.

XXVI.

Tunnels should be ventilated by shafts at intervals of not more than 200 yards.

XXVII.

While a train is passing through a tunnel, no beneficial ventilation can be obtained from shafts. The engine will leave behind it the impure air which it produces, and the passengers will be enveloped in it before it has time to ascend the shafts. Sufficient magnitude, however, may be given to the tunnel to prevent any injurious consequences from this cause. A disagreeable and inconvenient odour will be experienced.

XXVIII.

Tunnels on a level, the length of which do not exceed a third of a mile, will probably not be objectionable. Tunnels of equal length upon acclivities would be more objectionable.

I may observe generally that we have as yet little or no experience of the effect of tunnels on lines of railroad worked by locomotive engines, where there is a large intercourse of passengers. On the Leicester and Swannington railroad, there is a tunnel of about a mile long, on a part of the road which is nearly level; it is ventilated by eight shafts, and I have frequently passed through it with a locomotive engine. Even when shut up in a close carriage the annoyance is very great, and such as would never be tolerated on a line of road having a large intercourse in passengers. This railroad is chiefly used to take coals from some collieries near Swannington, and there is no intercourse in passengers upon it, except of the labouring classes from the adjacent villages: the engines burn coal, and not coke; and they consequently produce smoke, which is more disagreeable than the gases which result from the combustion of coke. This tunnel also is of small calibre.

On the Leeds and Selby railroad there is a tunnel, on a part which is nearly level, the length of which is 700 yards, width 22 feet, height 17. It is ventilated by three shafts of about 10 feet diameter and 60 feet high. There is an intercourse of passengers amounting to four hundred per day, upon this road, and, generally speaking, they do not object to go through the tunnel with a locomotive engine. The fuel is coke.

(_l_) In order to show the present state of railroad transportation in the United States, and enable our readers to compare it with the opinions and facts adduced by Dr. Lardner, we take the latest accounts from the Charleston and Hamburgh Railroad. The engines drag a train of cars which carry a load of 130 tons, and perform the distance (240 miles) in three days, travelling only by day-light. With these loads they mount planes having inclinations of 37 feet per mile. The same engines are capable of carrying passengers at the rate of 40 miles per hour, and often perform 30, but their average speed is limited by regulation to 20 miles per hour.

This railroad is remarkable for being the largest which has yet been constructed, and is besides an object of just pride, in as much as it was commenced at a time, when according to Dr. Lardner, the subject was but imperfectly understood even in Europe, and all its arrangements are due to native talent and skill, unassisted by previous discoveries in Europe.--A. E.

INDEX.

A.

Atmospheric air, elastic force of, 23

Atmospheric pressure rendered available as a mechanic agent by Denis Papin, 48

Atmospheric engine, first conception of by Newcomen, 61. Description of, 63. Advantage of over that of Savery, 69

B.

Barometer, the, 21

Barometer gauge, the, 123

Belidor, 133

Birmingham and London railroad, probable advantages to be derived from, 206

Black, Dr., his doctrine of latent heat, 76

Blasco de Garay, his contrivance to propel vessels, 42

Blinkensop, Mr., constructs a locomotive engine, 161

Boiler, methods for showing the level of water in the, 118. Its power and proportions, 297

Bolton, Matthew, his connexion with Watt, 88

---- and Watt, Messrs., immense expenditure of, in bringing their engines into use, 91

Booth, Mr., his method of using tubes to conduct heated air through locomotive boilers, 176. His report to the directors of the Liverpool and Manchester railway on the apparent discrepancies of Messrs. Walker and Rastrick's estimate of locomotive power, 189

Braithwaite and Ericsson, Messrs., their "Novelty" described, 175

Branca, Giovanni, his machine for propelling a wheel by a blast of steam, 45

Brewster, Dr., 79

Brunton, Mr., his improved furnace described, 130

C.

Canals, transport on, 208. Experiments with boats on, 209, Comparison of with railroads, 210

Cartwright, Rev. Mr., description of his improvements in the steam engine, 142

Cawley, John, 61

"Century of Inventions" by the Marquis of Worcester, 46

Chapman, Messrs., obtain a patent for working a locomotive by means of a chain, 162

Church, Dr., his steam carriage, 239

Cohesion, attraction of, 32

Condensation of solids, 28

Condensation by jet, accidental discovery of, 65

Cornwall, reports of duty of steam engines in, 303

Cotton, processes in the culture of, 18

Cylinder, its proportions, 300

D.

D valve, description of the, 113

Damper, the, 126

Duty of a steam engine, 291

Duty, reports of, in Cornwall, 303

E.

Eccentric; description of the, 111

Edelcrantz, the Chevalier, 127

F.

Farey, Mr., his statement respecting the variations in the work of different steam engines, 133

Fluids, property of, 21

Fly-wheel, introduction of the, 104

Four-way cock, description of the, 115

Fuel, table of the consumption of, in different locomotives, 180

G.

Governor, description of the, 105

Guericke, Otto, inventor of the air-pump, 70

Gurney, Mr., his steam carriage, 216

H.

Hackworth, Mr., description of his engine, the "Sanspareil," 173

Hall, Mr. Samuel, his patent steam engine, 248. Its advantages for navigation, 249. Its successful application, 250

Hamilton, Duke of, 88

Hancock, Mr. Walter, his steam carriage, 235

Heat, phenomena of, 29

Hero of Alexandria, description of his machine, 41

Hopper, the, or apparatus for supplying the fire-place with coals, 131

Hornblower, Mr., his double-cylinder engine, 134

Horse power and steam power, comparison between, 202

Horse power of an engine, 291. Method of calculating it, 293

Howard, Mr. Thomas, his patent steam engine, 253. Its advantages in navigation, 256

Huskisson, Mr., 154

I.

Inclined planes, their injurious effects on railroads, 194. Methods proposed to remedy these, 194

India, steam communication with, 271

K.

Kendal and Preston canal, speed of boats on, 209

L.

Leeds and Selby railroad, 317

Leicester and Swannington railroad, 317

Leupold, his "Theatrum Machinarum," 116. His engine described, 147

Liquids converted into vapour by the application of heat, 27. Difference of temperatures of, 35

Liverpool and Manchester railroad, effects of the introduction of steam transport on, 152. Want of experience in the construction of the engines, 154. Proceedings of the directors, 167. Premium offered by them for the best engine, 169. Experiments made on, 183. Passengers the chief source of profit to the proprietors, 204

Liverpool and London, supposed advantages from the connexion of these places by railroad, 206

Llangennech coal, its economy, 267

Locomotive engines, description of the "Rocket," 171. The "Sanspareil," 173. The "Novelty," 175. Mr. Booth's method of using tubes to conduct heated air through boilers, 177. Mr. Stephenson's method of subdividing the flue, 179. Amount of fuel consumed in, 180. Progressive improvement of, 180. Description of an improved form of engine, 181. Circumstances on which their efficiency depends, 183. Experiments with, on Liverpool and Manchester railroad, 184. Defects of, 186. Improvement in the method of tubing, 188. Proposed methods for working them on levels and inclined planes, 194. Extraordinary speed and power of, 204. Their introduction on turnpike roads, 213

Locomotive power, expense of, 188

Locomotive boilers, improved form of, 177

M.

Machines, definition of, 19

Manufactures, motions required in, 19

Morgan, Mr., his patent paddle-wheel, 259

Morland, Sir Samuel, his application of steam to raise water, 47

Motion, a primary agent in the cultivation of cotton, 18. Variety of, 19

Murray, Mr., description of his suggested slide valve, 113

N.

Newcomen, Thomas, and John Cawley, turn their attention to the practicability of applying steam engines to the drainage of mines, 61

Newcomen, Thomas, his construction of the atmospheric engine, 63

"Novelty," description of the, 175

O.

Ogle, Mr., his steam carriage, 239

Oldham, Mr., his modification of the self-regulating furnace, 132

P.

Paddle-wheel, the common one, 257. Mr. Morgan's patent one, 259

Papin, Denis, his contrivance, by which atmospheric pressure is rendered available as a mechanical agent, 48. Description of his steam engine, 71

Parallel motion, description of the, 95

Piston, its velocity, 302

Post-office steam packets, their speed, 268

Potter, Humphrey, his contrivance for working the valves, 67

Power of a steam engine, how estimated, 291

R.

Railroads, first introduction of locomotives on, 151. Important effects to be expected from their adoption, 155. Imaginary difficulty respecting the progression of carriages on, 160. Various methods resorted to, to remedy this supposed difficulty, 161. One of these methods described, 162. Comparative estimate of the expenses of locomotive and stationary engines, 168. Difficulties arising from changes of level, 192. Their great extension, 206. Comparison of, with turnpike roads, 213. Inclined planes on, 194

Railway speculators, plain rules for, 307

Roads, their resistance to draft, 213. Compared with railroads, 213

Robinson, Dr., 73

Roebuck, Dr., assistance rendered by him to Watt, 87. His embarrassments, 88

"Rocket," description of the, 171

S.

Savery, Thomas, obtains a patent for an engine to raise water, 49. His discovery of the principle of condensation, 49. Constructs the first engine brought into operation, 50. Description of, 51. Inefficiency of, 57. Great consumption of fuel necessary in his engines, 60. Different purposes to which he proposed to apply the steam engine, 61. Limited power of his engine, 69

"Sanspareil", description of the, 173

Smeaton turns his attention to the details of the atmospheric engines, 73

Solids converted into liquids by the application of heat, 27

Solomon De Caus, description of the apparatus of, 43

Somerset, Edward, Marquis of Worcester, invention of the steam engine ascribed to him, 45. Description of his contrivance, 45. Similar to Savery's, 46. His "Century of Inventions," 46

Steam carriages, Mr. Gurney's, 216. Mr. Hancock's, 235. Mr. Ogle's, 238. Dr. Church's, 239

Steam, its properties described, 30. Its mechanical power in proportion to the water evaporated, 277. Its volume, 279. Its quantity of heat, 279. Its power in respect of fuel, 280. Its expansive action, how advantageous, 280. Combination of expansion with condensation, 285. High-pressure, its expansive action, 288. Examples illustrative of its mechanical force, 305

Steam engine, first mover in, 19. Physical effects connected with, 20. Claims to the invention of, 38. Efficacy of, as a mechanical agent, 39. First brought into operation by Savery, 50. Its inefficiency, 58. First proposed to be applied to the drainage of mines, 61. Accidental discovery of condensation by jet, 65. Further improvements by Humphrey Potter and Beighton, 67, 68. Description of Papin's engine, 71. First experiments of Watt and subsequent improvements, 73. Dr. Black's theory of latent heat, 76. Watt's method of condensation, 76. Further improvements of Watt, 77. Description of Watt's single-acting engine, 80. The cold water pump, 86. The hot water pump, 86. Erection of a specimen engine at Soho, and gradual demand for them, 89. The single-acting engine inapplicable to manufactures, 91. The double-acting engine, 92. Invention of the parallel motion, 95. Introduction of the rotatory motion, 100. The fly-wheel, 104. The governor, 105. The throttle valve, 105. The eccentric, 111. The D valve, 113. The four-way cock, 115. Methods for ascertaining the level of water in the boiler, 118. The engine made to feed its own boiler, 120. Waste of water prevented, 121. The steam gauge, 122. Barometer gauge, 123. The damper, 125. Methods proposed for preventing the waste of fuel, 128. Mr. Brunton's furnace described, 130. Mr. Oldham's modification of the self-regulating furnace, 132. Improvements by Hornblower and Woolf, 134. Description of the improvements of Mr. Cartwright, 142. High-pressure engines, 145. Leupold's engine described, 147. Construction of the first high-pressure engine by Messrs. Trevithick and Vivian, 148. First application of the steam engine to propel carriages on railroads, 151. How applied to navigation, 242. Marine engine; its form and arrangement, 243. Mr. Howard's patent engine described, 253. Mr. Hall's engine described, 248

Steam gauge, the, 122

Steam navigation, incredulity which existed respecting, 159. The limit of its present powers, 264

Steam vessels, their average speed, 265. Their average consumption of fuel, 265. Proportion of their power to their tonnage, 266. Speed of post-office packets, 268. Iron steam vessels, 269. American vessel called the "Cigar Boat," its great speed, 270

Stephenson's, Mr., description of an engine constructed by him, 164. Premium awarded to this engine by the Liverpool and Manchester Railway Directors, 170. His method of dividing the flues, 179

Stephenson and Lock, Messrs., appointed by the Directors of the Liverpool and Manchester Railroad to make reports on the merits of various railroads, 167

Sun and planet wheels, 101

T.

Thermometer, description of, 24

Throttle valve, use of, 104

Traction, force of, on a railroad, 192

Tredgold,70

Trevithick and Vivian, Messrs., construct the first high-pressure engine used in this country, 148

U.

United States, steam communication with, 274

V.

Vacuum, production of, by experiment, 37

Vapour, elastic, force of, 35

Valves, Watt's method of working the, 109

W.

Walker and Rastrick, Messrs., apparent discrepancy of their estimated expense of locomotive power, 189

Washborough takes out a patent for Watt's invention of the rotatory motion, 100

Water, sea, injurious to marine boilers, 245. How remedied by blowing out, 246

Watt, James, important discoveries of, 39. His acquaintance with Dr. Robinson and first experiments on the steam engine, 73. His subsequent improvements, 75. His method of condensation, 76. His first introduction of the air-pump into the steam engine, 77. Further improvements, 78. His difficulties, 78. Description of his single-acting engine, 80. His introduction to Dr. Roebuck, 88. Erects his first engine on the estate of the Duke of Hamilton, 88. After further improvements, obtains a patent for this engine, in conjunction with Roebuck, 88. His difficulties owing to Dr. Roebuck's failure, and subsequent connexion with Bolton, 88. Obtains an extension of his patent, 89. Ingenious invention of, to determine the rate of remuneration he should receive, 89. His invention of the parallel motion, 95. His method for producing a rotatory motion anticipated by Washborough, who takes out a patent for it, 101. His contrivance of the governor, 104. His method of working the valves, 109. His suggestion of the D valve, 113

Wood, Mr. Nicholas, 168

Woolf, Mr., his improvements in the steam engine, 134. Obtains a patent for the double-cylinder engine, 137

* * * * *

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MATHEMATICS FOR PRACTICAL MEN;

BEING

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SECOND EDITION, CORRECTED AND IMPROVED.

_Extract of a Letter from_ WALTER R. JOHNSON, _Professor of Mechanics and Natural Philosophy in the Franklin Institute_.

"This treatise is intended and admirably calculated to supply the deficiency in the means of mathematical instruction to those who have neither time nor inclination to peruse numerous abstract treatises in the same departments. It has, besides the claims of a good elementary manual, the merit of embracing several of the most interesting and important departments of Mechanics, applying to these the rules and principles embraced in the earlier sections of the work.

"Questions in Statics, Dynamics, Hydrostatics, Hydrodynamics, &c., are treated with a clearness and precision which must increase the powers of the student over his own intellectual resources by the methodical habits which a perusal of such works cannot fail to impart.

"With respect to Engineering, and the various incidents of that important profession, much valuable matter is contained, in this volume; and the results of many laborious series of experiments are presented with conciseness and accuracy."

_Letter from_ ALBERT B. DOD, _Professor of Mathematics in the College of New Jersey_.

"MESSRS. CAREY & HART,

"Gentlemen,--I am glad to learn that you have published an American edition of Dr. Gregory's 'Mathematics for Practical Men.' I have for some time been acquainted with this work, and I esteem it highly. It contains the best digest, within my knowledge, of such scientific facts and principles, involved in the subjects of which it treats, as are susceptible of direct practical application. While it avoids such details of investigation and processes of mathematical reasoning as would render it unintelligible to the general reader, it equally avoids the sacrifice of precision in its statement of scientific results, which is too often made in popular treatises upon the Mathematics and Natural Philosophy. The author has succeeded to a remarkable degree in collecting such truths as will be found generally useful, and in presenting them, in an available form, to the practical mechanic. To such, the work cannot be too strongly recommended; and to the student, too, it will often be found highly useful as a book of reference.

"With much respect, "Your obedient servant,

"ALBERT B. DOD,

"Professor of Mathematics in the College of New Jersey. "_Princeton, Nov. 11, 1834._"

_Extract of a Letter from_ EDWARD H. COURTENAY, _Professor of Mathematics in the University of Pennsylvania_.

"The design of the author--that of furnishing a valuable collection of rules and theorems for the use of such as are unable, from the want of time and previous preparation, to investigate mathematical principles--appears to have been very successfully attained in the present volume. The information which it affords in various branches of the pure and mixed Mathematics embraces a great variety of subjects, is arranged conveniently, and is in general conveyed in accurate and concise terms. To THE ENGINEER, THE ARCHITECT, THE MECHANIC--indeed to all for whom _results_ are chiefly necessary--the work will doubtless form a very valuable acquisition."

_Letter from_ CHARLES DAVIES, _Professor of Mathematics in the Military Academy, West Point_.

"MILITARY ACADEMY, West Point, May 14th, 1835.

"_To Messrs. E. L. Carey & A. Hart_,--

"The 'Mathematics for Practical Men,' by Dr. Gregory, which you have recently published, is a work that cannot fail to be extensively useful.

"It embraces, within a comparatively small compass, all the rules and formulas for mathematical computation, and all the practical results of mechanical philosophy. It is, indeed, a collection of the useful results of science and the interesting facts which have been developed by experience. It may safely be said, that no work, of the same extent, contains so much information, with the rules for applying it to practical purposes.

"I have the honour to be, "With great respect, "Your obedient servant,

"CHARLES DAVIES,

"_Professor of Mathematics_."

_Extract from a Letter from_ J. A. MILLER, _Professor of Mathematics in Mount St. Mary's College, Emmettsburg, Md._

"Since the London edition of Gregory's Mathematics for Practical Men appeared in this country, it has been much used in this institution. The accuracy of its definitions, its beautiful systematic arrangement, the many simplified and facilitated methods which it proposes, and its highly practical character, must recommend it strongly to public patronage, as one of the very best works which have lately issued from the press. I have examined your edition of this valuable work sufficiently to say with confidence that it is very accurately printed."

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[Transcriber's note: Only obvious printer's errors have been corrected (e.g.: 3 s instead of 2, etc.). The author's spelling has been maintained and inconsistencies have not been standardised.

The advertisement page has been move from the front to the end of the book.

Other corrections made:

--Page x: "the wealth of rations" has been replaced by "the wealth of nations".

--Page 17: "Pressure of Rarified Air." has been replaced by "Pressure of Rarefied Air."

--Page 98: "This beautiful contrivance, which is incontestibly" has been replaced by "This beautiful contrivance, which is incontestably".

--Page 100: "the working beam no longer used" has been replaced by "the working beam is no longer used".

--Page 223: "is attended with peliar difficulty" has been replaced by "is attended with peculiar difficulty".

--Page 271: "The projecter is now employed in" has been replaced by "The projector is now employed in".]