MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



the railway system. The locomotive engine will ever 

 remain as an invention entirely distinct from those 

 created by the genius of Watt. It is in reality in- 

 dependent of his great principle of separate conden- 

 sation. It has a power of adaptation and a perfection 

 of performance more astonishing than any contrivance 

 of our time, except perhaps the electric telegraph. 

 In 1552, Jerome Cardan took twenty- three days to 

 travel from London to Edinburgh; that the same 

 should be done 300 years later in eleven hours, and 

 every day, is a fact as striking as any which the pro- 

 gress of science presents. Whilst to Trevithick and 

 George Stephensou we are mainly indebted for these 

 results, the theory of the steam-engine is still in ar- 



rear. To M. de Pambour we are indebted 1 for by M. de Pnm 

 far the best account of the elements of force contained b ur on th 

 in the locomotive, and of the resistances which they i como- 

 have to overcome ; but it is not to be doubted that tives. 

 much yet remains to be done in this direction. 



George Stephenson died 12th August 1848, at the (407.) 

 age of sixty-eight, and generally respected for his Stephensoi 

 private character as well as for his talents. His son 

 had the honour of completing the second great railway 

 work in Britain, from London to Birmingham, and 

 by the invention of the tubular bridge, described in 

 a previous section, he has added the most important, 

 as well as the most scientific auxiliary to the exten- 

 sion of railways since 1830. 



6. Hydrodynamics, DUBUAT, VENTUKI, Professor STOKES. Friction and Resistance of Fluids. 

 MM. WEBER, Mr SCOTT RUSSELL. Propagation of Waves. Influence on Canal Naviga- 

 tion. MM. FouRNEYROff and PONCELET. Improved Hydraulic Machines ; Turbine. Reference 

 to the subject of Capillary Attraction. 



Hydrody- 

 namics 



(408.) There are few subjects less adapted for the kind 

 Progresa of o f Discussion which I have adopted in this Disserta- 

 tion than Hydrodynamics, whether in its abstract or 

 practical form. Not only is it difficult to fix upon 

 individuals who, in the more recent progress of the 

 subject, have attached themselves to it in so especial 

 a manner as to have impressed the science with the 

 individual character of their own minds, but the pro- 

 gress made in either branch has been of a remarkably 

 fragmentary kind, usually bearing upon the solution of 

 individual problems, and tending to the improvement 

 of particular machines. It must be owned, too, that 

 however important in practice may be the efficiency 

 of a water-wheel or the discharge of a pipe, the so- 

 lution of such problems does not present the attrac- 

 tive interest which attaches to many less difficult ones 

 in Natural Philosophy. As regards more general pro- 

 blems of which a direct solution from first principles 

 might appear possible, it has been found that these 

 are as yet so limited as to give a character (which is 

 generally admitted) of great barrenness to the theo- 

 retical investigations. 



While, then, I shall endeavour, in conformity with 

 my general plan, to preserve something of the bio- 

 graphical character in the history, suppressing details 

 and many minor and even some important steps, 

 this section will necessarily have somewhat of a frag- 

 mentary character, and its deficiencies must be sup- 

 plied by a reference to the numerous articles of the 

 Encyclopaedia which treat more or less fully of these 

 subjects and their history. 



(409.) 



1. Friction and Resistance of Fluids. The first 

 name I shall mention is that of the Chevalier Du- 



(410.) 

 Dubuat 



Friction , . 



and resist- B UAT, who has the signal merit ot having attri- 



ance of buted due importance to, and of having considered 

 fluids. 



with much sagacity, the effects of the friction of 

 fluids against their own particles, and against the 

 sides of the solid bodies used to confine them. He 

 had the full advantage of an acquaintance with the 

 Abbe Bossut's excellent experiments and judicious 

 writings, but he was, I believe, the first who suc- 

 ceeded in ascribing to the different forces which act 

 on fluids in a state of uniform motion their effective 

 share in determining their velocity. I refer particu- 

 larly to the discharge of pipes and of rivers. Du- Theory of 

 buat showed that when the motion of water in such rivers * 

 circumstances becomes uniform, the accelerating force 

 which acts is the measure of the total resistances to 

 the fluid motion, whether arising from the inequali- 

 ties of the bed or the viscosity of the fluid. These re- 

 sistances are assumed to be proportional to the square 

 of the velocity. Since they are exactly in proportion 

 to the length of the pipe or channel, and since the 

 moving pressure increases in the same proportion, the 

 velocity is independent of the length of the pipe, whilst 

 the inclination remains the same a simple result not 

 previously noticed. In the case of a pipe the head 

 or superincumbent pressure may be divided into two 

 parts ; one, requisite to force the water into the tube 

 with the requisite velocity, which is independent of 

 the distance to be travelled; the other, which balances 

 the resistance due to the length of the pipe, which 

 for a given diameter varies as the length, or if the 

 slope be constant is independent of the length. 



The relation of the area of the stream to the peri- 

 meter or rubbing surface of the channel is then taken 

 into account. This ratio is called by some writers the depth. 

 mean hydraulic depth. The manner in which Dubuat 

 derives his formula (which I shall not here set down) 

 from direct experiment, guided by a few general no- 

 tions of theory, is a very good specimen of this kind 



1 The Theory of the Steam-Engine (1839), and A Practical Treatise on Locomotive Engines (1840), by the Comte F. M. G. 

 Pambour. 



