1818.1 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



43 



ON WING WALLS OF BRIDGES. 



By R. G. Clark, C.E. 



As the drawing of wing- walls to railway bridfres oifers some 

 difficulty when the embankments or cuttings are very high, to 

 obviate this is the object of the present paper, which relates to the 

 investig-ation of some simple formuliB to determine the angles 

 made by the exterior lines of wing walls with the face of a bridge; 

 the phine of projection lieing taken on a level with the rails or 

 road, when the latter is level. 



There are two cases to be considered. — 1st. Mnien the coping of 

 the wing wall makes a given angle w ith the face of the bridge, or 

 is parallel to the abutment, as in the case of a skew bridge. — 

 2ndly. M'hen the coping is perpendicular to the face of the 

 bridge. 



1st. Let B H be the line of the face of the bridge on H B E D, 



the plane of projection as 

 before mentioned ; C D the 

 exterior top line of wall ; C e 

 the given batter, perpendicu- 

 lar to B D. The / H C D 

 being given, or D C drawn 

 parallel to B B', as in the case 

 of a skew bridge, draw E D 

 parallel to B II ; and BE, CF, 

 respectively, perpendicular to 

 E D. For the sake of sim- 

 plicity, we will first determine 

 the iCDB. 



Let the slope of embank- 

 ment or cutting be as »h to 1, 

 and the batter of wing wall 

 as 1 to n ; height of slope equal h. Now. / C D E = Z H C D. 

 Let Z C D E ^ e. Also, base of slope C F r^ m h ; and batter 



C e of wing wall = - A. 



r; 



D 



Then, by the right-angle triangle C F D, we have 



772 h 



sin e 



1 



^. = DC. 



sin e 



Also, by triangle C e D, right-angled at e, we have 



mh 

 sin 9 



1 



sine 



nat. sin ZCDB (1). 



n mr. 



.-. ZHBD= /HCD or ZCDE - ZCDB. 



Eiample. Given the angle of obliquity H C D = 20°, slope 

 1^ to 1, and batter 1 in 5, to determine the angle of wall H B D : 



By formula 



nat. sin 20' 



2 X -34202 



1* 



X 5 15 



therefore, Z H B D = 20° - 2= 



= -04560 = nat. sin 2° 57 1 



37^' = 17° 22' 30" required. 



2ndly. When the coping is perpendicular to 

 the face of the bridge. 



Then sin e := 1 ; 

 consequently, sin Z C D B = — . 



Hence, cos C B D := 



(2). 



Then nat. cos Z C B D = ^ = -2 : 



E.ramples. 

 WTien the slope is 1 to 1, and batter 1 in 5. 

 nat. cos of 78° 27'. 

 When the slope is li to 1, and batter 1 in 5. 



Then ZCBD = 82° 20'. 

 When the slope is 2 to 1, and hatter 1 in 5. 



Then Z € B D = 84° 15'. 

 From the above it appears, that the actual height of the slope, 

 and the batter in feet, &c., have no occasion to be taken into con- 

 sideration ; but only their respective ratios, as above given. 



RAILWAY AND STEAM NAVIGATION DEFENCES. 



The course which the Duke of Wellington has thought fit to 

 take, in furtlierance of tlie measure of increasing the army under 

 his command, has given a new strength to the alarmist party. We 

 say, advisedly, that the Duke's letter to Sir John Burgoy'ne can 

 only be taken as the statement of an advocate, using e\'erV means 

 to make out a case ; for there is evidence enough in that letter to 

 show the impracticability ot an invasion, if it were consistent to 

 suppose that a commander so experienced could countenance a 

 scheme, which the youngest statt'-officer knows is in no way 

 feasible. In considering the subject, we do not think it necessary 

 to analyse the Duke's letter, because we do not look upon him as 

 a believer in the invasion sclieme ; but we shall take up the ques- 

 tion upon its own merits, which are certainly small enough, com- 

 pared with tlie clamour which has been made by so many parties, 

 and of which tlie Commander-in-Chief has so' skilfully availed 

 himself, to further the \'iews of his own department. 



It is one of the consequences of thirty-two years of peace, that 

 the present generation know little of war or of military affairs 

 and it is therefore open to ignorant or restless oflBcers to impose 

 upou them statements, which do not meet with the countenance of 

 men well informed in tlieir own profession, and which are not con- 

 sistent with liistoric proof. With the public an officer is taken as 

 an aiithority in virtue of his epaulettes ; but, nevertheless, he is as 

 an officer no more an authority on this question of invasion, than 

 the most ignorant civilian. It is one of the misfortunes of the 

 English army, that there is no guarantee for the qualifications of 

 its officers ; and, notwithstanding the growing desire of improve- 

 ment among military men, it cainuit be denied that it is much rarer 

 to find a man w ell acquainted with his profession than otherwise, 

 for there is no security, and it may be said no encouragement, for 

 proficiency. In the navy, and in the artillery, an examination 

 must be passed ; but, under the system by which the army is offi- 

 cered, except the few C(dlege cadets, a man may be put in command 

 of an army, whose only (jualification is that he can manoeuvre a 

 battalion on parade. Neither is the service of the English army 

 calculated to qualify an officer for European warfare, for the staff 

 arrangements even of an Indian campaign will give no schooling 

 for a war in tlie old battle-field of Flanders. One of the defences 

 we most want is a good staff of officers, and money cannot be 

 better laid out than in enlarging the military colleges, and en- 

 couraging the studies of officers. In the meanwhile, we hope the 

 public will not allow themselves to be frightened out of their wits 

 by men who know no more of the organization of an armv of fifty 

 thousand men tlian a drummer-boy does; and, at any rate, to 

 accept with caution any statements which have not the support of 

 common sense and historical evidence. 



It is very easy to start with the hypothesis of 50,000 Frenchmen 

 on the Sussex coast, and to talk of the capitals of France, Austria, 

 Russia, and Prussia having fallen into the hands of an enemy; but 

 it is so difficult to conceive how a French army of 50,000 nien, or 

 of any other force, could be brought to London, that any general 

 being ofl^ered the command of such an expedition, would give it up 

 in despair. In order that a French army may land upon the 

 English shore, there must be no political disorganization in France, 

 and there must be political disorganization in England. Our great 

 protection hitherto against invasion from France, has been the 

 political disorganization of that country by the League, the Pro- 

 testants, the Camisards, the Girondists, or the Chouans, or by the 

 irruption of Prussians, Spaniards, or Savoyards. Napoleon never 

 hoped to be able to make an effectual invasion of this country, 

 unless he could make a piditical diversion, by securing the neu- 

 trality of parties in opposition to the government. How futile 

 was that dependence is well known; and though some may, in the 

 present time of calm, believe that political factions might here- 

 after be brought to sympathise with an invader, yet such coalition 

 flould become impossible when war shall break out, and the old 

 feelings of bitter hatred be awakened. This is a disturbing in- 

 fluence which cannot be readily overcome. There is nothing more 

 difficult than to overcome a people in their own country, vvith 

 whatever force, if united in resistance. France will give the ex- 

 ample. If, in 1814 and 1815, the allies were able to make their 

 way to Paris in the then political disorganization of the country, 

 yet, in the early part of the war, under the Duke of Brunswick, 

 though France was unprepared, the invaders were driven back with 

 loss. 



The circumstances under which an invasion of England will be 

 practicable are — the union of the French, High Dutch, and Rus- 

 sians, the destruction of the naval power of England, our political 

 disorganization, and the agreement of a large part of the people 



7* 



