ART. 30. Lines of Socket-jointed Pipe-The combination of two or more resist- 30A. Joints Turned and Bored-The limited tensile strength of such joints 32. The Measurement of Hydrostatic Pressure-The mean pressure and the total pressure upon plane surfaces of regular figure. 33. The Centre of Action-Its position upon the same plane surfaces when 34. Vertical Walls of Irregular Figure-Example of the calculation for the 35. Surfaces submerged in Deep Water-General method of treatment 36. Contrary Horizontal Pressures-Effective pressure on a lock gate 37. Hydrostatic Pressure upon Inclined and upon Curved Surfaces-The horizontal and vertical components-Vertical buoyant pressure upon 77 38. Equilibrium of Floating Bodies in General-Special application to 41. Vertical Motion under the Vertical Forces-Examples of stable, in- 42. Lines of Action of the Vertical Forces-The section of the vessel con- sidered as a diagram of buoyant pressures-Centre of gravity and 43. Conditions of Equilibrium in Still Water-Righting moments and up- 44. Stability of a Closed Vessel wholly Submerged, and of a submerged 45. Stability of a Floating Gas-holder, and of an Inflated Bridge Caisson 46. Stability of a Water-logged Vessel with Thin Sides 47. Stability of a Cylindrical Pontoon floating on its Side-The fixed 48. Stability of a Rectangular Pontoon in the upright position-The curve of buoyancy-Calculation of its co-ordinates and of the metacentric 51. Cylindrical Vessel floating on End-Its stability or instability 52. Annular Vessel, or Double-skinned Cylindrical Caisson-Its metacentric 99 53. Negative Metacentric Height-Case of submerged tank partially filled, or 54. Effect of Water-ballast in Compartments-Calculation of the reduced BENDING STRESSES IN FLOATING PONTOONS. 55. Distribution of the Vertical Forces-The buoyant pressure generally known but affected by elastic deflection 56. General Expressions for the Bending Moment and the Vertical Shearing 57. Pontoon carrying a Central Load-The stresses calculated for an in- flexible and for a flexible pontoon. 58. Pontoon carrying a Pair of Equal Loads symmetrically disposed-Calcula- tion of the bending stress and construction of the curve of deflection. 59. A Series of concentrated Loads imposed at Three or More Points at 61. Pontoon carrying the Weight of a Long Girder-Relative deflections of 62. Long Pontoon carrying a Short Ship or Girder 63. Greatest Bending Moment due to the opposed vertical forces APPENDIX A. EXPERIMENTAL MEASUREMENT OF DISPLACING FORCES. 107 1. Equilibrated Fluid Arch or Vertical Bend-Description of apparatus 135 INTRODUCTION. We often hear it said that engineering is gradually assuming the character of an exact science; or, to speak more correctly, that the practice of the engineer is becoming little else than an application of the exact sciences; and the saying conveys one of those half-truths which are so apt to mislead people when they do not know the other half of the truth. Of course engineering is something more than a science, and more than an application of all the sciences, for some of its weightiest and most difficult problems are unknown to any of them. Science, for example, has nothing to say about the adaptation of means to an end-a question which presents itself at every `turn, and constantly demands the engineer's most careful study in the execution as well as in the design of his works. In the preparation of his design, it is perhaps almost indispensable that the principles of mechanical theory should be consulted; but the first essential and the most important object to be kept in view, is not compliance with scientific rule, but rather the achievement of a definite and clearly realized purpose. And the purpose to be achieved in the design of each detail is not generally a simple or a single purpose, but is often a legion of mechanical purposes; while the conditions to be observed are not only those which theory prescribes, but include a multitude of others which are of equal importance. The mental faculty by whose aid the engineer marshals before him, in their right order, the purposes to be achieved and the conditions to be observed, and by which he goes on to select or devise the right means for the attainment of his end, is a faculty that cannot be cultivated by the usual methods of the educationist, can scarcely be acquired by a university training (though it may perhaps be exercised), and cannot be very much strengthened by the reading of books. B However, science can tell us what it knows about law; and the engineering purpose can never be achieved except by a careful compliance with mechanical laws. If engineering does not consist in a knowledge of these unalterable principles, yet it would be absurd to underrate their importance. It is perfectly true, also, that in modern times the practice of engineers is, more than ever, guided by a constant reference to theoretical calculations; and in no branch of construction is this to be seen more conspicuously than in works of hydraulic engineering, for here calculations are constantly being made to determine a number of questions on which must depend the broad outlines, the minute details, and almost every feature of the work. The writings that exist on this subject show us, indeed, that it forms one of the oldest parts of engineering theory; and from the time of Leonardo da Vinci men have been striving to reduce to order the principles that govern the flow of water, while the aqueducts of old Rome seem to prove that this people must have known a good deal more about the matter than we sometimes give them credit for. Such knowledge as they possessed must certainly have been derived mainly from experimental observations, and there is evidence enough to show that its extent was somewhat limited; but we all know that since their time the exact sciences have made enormous progress. And yet it is a remarkable fact that, so far as this particular question is concerned, the exact sciences have contributed nothing to the development of engineering theory as it is now understood and employed. In the science of hydrodynamics, the exact methods of the mathematician lead to conclusions which are known to be so far from the truth that engineers can never rely upon them; and it is just as true to-day as it was in the time of Galileo, that our calculations must of necessity be based upon the observed results of experiment. But if science has failed to explain the natural laws which govern the flow of water, the labours of hydraulicians have added greatly to the number and to the accuracy of experimental observations. To this work of patient observation and measurement, it must be confessed that very little has been contributed from our own country, but a great deal has been done, and is still being done, in France, Germany, and America. The tables that were calculated from the older formulæ are scarcely accurate enough to satisfy modern requirements, and may be rendered more exact by a careful collation of the evidences which have been recorded in the results of these later experiments; while it is also possible to convey those results in a form that would be more useful for practical purposes than the somewhat elaborate formulæ by which they have been expressed. If we turn to another series of problems, which are related, not to the flow, but to the pressure of water, the state of our existing knowledge and the methods of present practice must be very differently described. Here the calculations of the engineer rest upon the surest foundations, for the principles of hydrostatics have long ago been established, and can never be changed. The calculations, therefore, can be made with the utmost confidence, upon purely rational principles, and with the certainty that they will not be vitiated by any errors of experimental observation. The engineer will be concerned mainly with the calculable effects of hydraulic pressure upon the various structures or machines that may form part of his great constructive works; and although the principles of hydrostatics are in themselves exceedingly simple, yet their application to his own practical purposes will be as complex as are the varying forms which his structures may assume, and the varying conditions under which they have to be executed. The works that he is engaged upon may be designed for the collection and storage of water, or for its conveyance in aqueducts and open channels, or through tunnels, culverts, and pipe-lines-either for the supply of towns, the drainage of towns and districts, or the irrigation of lands. In other cases they may relate to the establishment of water-courses for purposes of navigation, the correction of rivers, and the prevention of floods or perhaps to the utilization of water-power, or the hydraulic distribution of power from central stations. And the principles of hydraulic engineering will have their application over a still wider field, which must include many works of harbour-construction, the sinking of foundations in deep water, and the transport of heavy loads upon floating pontoons. In connection with all these matters, the engineer will have to deal with the effects of hydraulic pressure under a great variety of conditions. Sometimes the calculations will be very |