292 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[OCTOBEB, 



w}iat requires consideraMe ptudy and foresijjht. In temporary 

 exhiliiticins, pictures must beliunp up as well as the}' can be. The 

 dispiisini; them on the walls is of necessity a work of such hurry, 

 that it is little to be wondered at if it is frequently attended with 

 awkward mistakes, such as putting a fr^od paintiui; nearly (uit of 

 sight, and an inferior one just upon the line. Even if it be de- 

 tected, there is no time for correctiniar the error, because to do 

 so mifrht render it necessary to alter the situations of a score of 

 other pictures. 



In a permanent gallery, on the contrary, more especially one 

 claiming to be considered a public museum fif art, where nothing, 

 it is to presumed, is admitted but what is worthy of being studied 

 — at least, of being noticed as a work of art, — the utmost attention 

 ought to be given before-hand to what is requireil by the collection 

 itself. Should this last be already fully formed, to provide pro- 

 perly for it becomes a coniparatix'ely easy task ; whereas, for 

 one that is increasing, regard should be had to future growth. 

 When Mr. Wilkins — or rather, perhaps, those who employed him — 

 took measure of it, our national collection was merely in its 

 infancy. Thanks to Mr. Vernon, tlie child has nearly all at once 

 started up into a tall stripling, — has quite outgrown his former 

 " fit," which suit suits him no longer ; so Mr. Barry is now it 

 seems to enlarge it, and convert it as well as he can into a becoming 

 togavirilis. If he can do so without reclaiming from the Academy 

 the piece of stuff they have got possession of, he must have far 

 more talent in point of contrivance than most of his professional 

 brethren. 



After all, we may possibly have been put quite on a wrong 

 scent. Should which turn out to be the case, all we can say is, 

 that the mistake does not lie at our door. We leave those from 

 whom we got it to trace out tlie author of it ; nor should we be 

 greatly surprised to find it traced home— if mistake it really be — 

 to that confounded, universal mischief-maker, Mr. Nobody i 



COLLISION OF TRAINS.— No. II. 



In our last paper (p. 197), we considered the law and amount of 

 collision in a train of carriages of equal weights, and provided 

 with a single engine in front. We now propose to examine the 

 effect of an engine behind, the other circumstances of the problem 

 remaining the same. 



As a first and introductory e.xample, let us suppose a single car- 

 riage, weight i tons, having a pair of buffers in front, with a foot 

 play to each, and each with an extreme strength of 4 tons (the law 

 of resistance of the buffers being assumed to vary as their com- 

 pression), to impinge on a fixed obstacle with a velocity of 60 feet 

 per second. Let ns now determine how much of this velocity will 

 be destroyed liy the time the buffers have ceased to act. 



Let m be the mass of the carriage ; p, the jiressure on the head 

 of either buffer when it is compressed to an extent x ; v, the 

 velocity, in seconds, of the carriage; — then, the mass of the buffer 

 being neglected as small in comparison with the mass of the 

 carriage, 



dv 

 mv-r- = — 2 p. 

 tf.r 



Now, i tons is the value of p when x z=. I ; and since p has 

 been assumed to vary as x 



dv 

 p =: ix ; :. mil y- = - Sx ; :. mv- =z c — 8 «■'. 

 ax 



If the accelerating force of gravity be taken at 32 feet per 

 second. 



4. 

 32 



1 



Sx'; 



ti' =: 8c- 6 4.r'. 



Wlien .r = 0, « = 60; .•. Sc = 3600. 



When X = 1, the buffers cease to act, and v- = 3600 — 64; 

 or, V = 59^ nearly ; consequently, only half-a-foot of velocity is 

 destroyed. 



Let us next consider the case of a train of n carriages, each 

 provided with a pair of buffers before and behind ; and with an 

 engine, weight r tons, attached to the last carriage ; and let us 

 suppose this train to impinge on a fixed obstacle at the rate 

 of V feet per second ; and from these data seek approximately 

 the amount of velocity destroyed in the rearward engine by the 

 time all the buffers are used up. 



In order to make the problem general, we will assume the 

 weiglit of the carriages each =: w, and the extreme strength of 

 the buffers m/i tons ; also their extreme play h feet. By the time 



the engine behind has moved forward a space .r, after collision has 

 commenced, let 2/) be the pressure on the buffers of the rearward 



p 

 engine. We shall now show that p is always less than , , where 



n' is the number of pairs of buffers, and P the pressure on any 

 buffer compressed to an extent x. For let x,, x^, x^, &c., be 

 the extent to wliich the buffers are simultaneously compressed, 

 reckoning from the carriage wliich first sustains the shock ; *iJ',, 

 nx^, ^lx.„ &c., the pressures of the liuffer-heads corresponding to 

 the compressions .»-,, x,^, x^, &c. Now we have shown in our last 

 paper that the pressures of the buffers, and therefore j-,, .r^, j',, 

 &c., decrease as we recede from the end of the train nearest 

 collision. 



.•. X, is > x^; X2 is > x^ ; &c. is > &c. 

 p — lix^r, pis < p.x„,_x; p\a < lix,,,-^; &c. is < &c. 



.•. n' p is < M {xn' + ^;i'-l + &c.) is < lix is < P; 



P 



.•. p IS < -. 



lux dx 

 h 



It 



IS < 



•.n'V 



pax IS < / ax IS < / 



n'h J n'h n' J n' 



Therefore, if v be the velocity of the rearward engine, by the time 

 the buffers are aU used up, 



— (V-— jj'-) is < 'Znn'h'-. 



As an example, let A = ], as before ; w = 19 ; :. n' =. iO (in- 

 cluding buffers of engines before and behind) ; r =:; 20; V =: 60 ; 

 f = 4. 



30 

 .-. V- — u- is < — X 320 is < 32 X 16 is < 512. 



If V = 60, .-. v' is > 3088; :.v is > 65. Or, the velocity of 

 the rearward engine has been diminished by less than 5 feet a 

 second. 



If V had been put ^ 30, which is equivalent to about 20 miles 

 an hour, still v would ha\e had a value of 20 feet a second, or 

 twelve miles an hour. In eitlier case, it is clear that the shock of 

 the engine behind would have been most destructive — in the first 

 case frightfully so. 



To recapitulate the results of our investigation, it a))pears, first, 

 that when a train with a single engine is violently checked, the first 

 carriage will sustain the greatest damage, and the effect of the 

 buffers will be to increase the number of blows on the first and 

 succeeding carriages, but to diminish their intensity. Secondly, 

 that when an engine is attached behind ; the last carriage after all 

 the buffers are used up — having first to sustain the shock of the 

 rearward engine proceeding with a diminished but still considera- 

 ble velocity, if the original \'elocity of the train had been great, — 

 will probably be the most seriously injured of all the carriages. A 

 double shock will in this case have passed along the train — at first, 

 by the sudden stoppage of the first carriages before all the buffers 

 are used up ; and then from the blow from the rearward engine 

 after alt the buffers are used up. 



Since writing the former paper on this subject, we have seen a 

 model of a break, by Mr. Bishop, which by an ingenious and simple 

 contrivance is capable of being applied to all tlie carriages simul- 

 taneously, and almost instantaneously. We earnestly recommend 

 the adoption of some such method of suddenly occasioning a 

 powerful retarding force, as a most efficient means of avoiding 

 casualties and coroners' inquests. 



J. H. R. 



M)TES ON ENGINEERING.— No. XI. 



By HoMEitsHAM Cox, B.A. 



The Strength of Hungerford Bridge. 



The security of a Suspension Bridge erected in the very centre 

 of the metrojiolis, and liable to .sustain the weight of a very large 

 number of persons, is a subject possessing a scientific interest 

 commensurate with its practical importance. The moment of the 

 question has been greatly increased by two independent circum- 

 stances — first, that it has been the subject of serious doubt and 

 scientific discussion ; and secondly, that the trafiic of the bridge 

 has recently received an important accession by the opening of a 

 railway terminus in its immediate vicinity. 



There are some parts of the theory of suspension bridges exceed- 

 ingly complicated and difficult, and others perfectly simple. Among 



