THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



43 



MOMENTUM OF FALLING BODIES, COLLISION, &c. 



Sib,— In further elucidation of my letter of last month, I beg to 

 ofter the following remarks, which I request you will be so obliging as 

 to insert. 



" Momentum is said to be (vide Hutton's Course of Mathematics, 

 Vol. II, page m, &c.) the power or force in moving bodies witli which 

 they strike any obstacle which opposes their motion :" and (page .'JH, 

 proposition 149) it is mid that " B being a body moving with the 

 velocity I', BV=M\s the momentum witli wliich it strikes anotlier 



body b :" — and an example is given of two bodies, Ji weighing o, and b 

 weighing .S, moving respectively witli velocities T'=;3 and i' = -2, which, 



it is said, would, after collision, move with velocities — ; y = '2^ 



■" ' b 



if previously moving in the same direction i 



liifin 



BV 



opposite directions, and 1 = IJ if 6 were at rest. Now I 



'^' n + b ^ 



hold this to be incorrect. I conceive the momentum of a body moving 

 with a given velocity, to be the smn of two similar forces (>n =: /* -j- 

 M), whereof ,a is the force that acts to overcome the ineitia of the 

 body and is measured by its weight (;J- =: b), and j\I is the force ne- 

 cessary to preserve the motion of the body at the given velocity ; 

 which force is in proportion to the product of the weight by the 

 velocity (M is as bv). — From the experiment detailed in my last letter 



I conclude that M = (ph>, where ^ is > ',- and < ~ nearly = #. 

 Hence m :=. b + ii bv ; and v in feet per second = ?, ('^^- \ — The 

 following would be the working of the problem .ibove rpioted. 

 Itithe momentum of ^ = 5 + ;} (5 X a) = •27i.|wlieie the formula 

 m ditto of 6' = 3 + 1 (3 X 2) = 1-2. j 's m = 6 + ^ bv. 



Making use of these values of the momenta and the formula 



r := 5 ( — r - ) applied to the various cases, we have 



" "^ "' ^ — X I = 2;a velocity when B and b moved in 



(I) 



(11) 

 (III) 



27i— 12 — S 



27i — 8 



the same direction. 

 X I = 5 velocity when they meet. 



X I =: If velocity when B was moving and b a 



rest before the collision. 

 These resulting velocities are very different from those given in 

 " Hutton's Course." — Experiment would decide which are correct. 

 Were the experiment, detailed in page 18 of this Journal, repeated 

 with good spring balances, and different weights let fall, a more exact 

 value of p would be obtained, and the formula ;7i := /* + iH = 6 -f- fbv 

 would be tested. 



Yours obediently, B. 



Errata. — Pago 18, line .34, for w; :=: J + M'"', read m := i + fbv, 



„ 49, insert between, and read equal to be- 



tween 10-7th3 and 13-8ths, &c. 



WOODEN PAVEMENT. 



Sir, — I was much gratified the other day, in passing along Oxford- 

 street, to see that a comparative trial is about to be made of various 

 kinds of pavement. It is only by laying down the different sorts in 

 juxtaposition, on a much frequented thoroughfare, that any thing like 

 a just estimate of their respective advantages can be made. I know 

 not whether the works now going on are under one particular supcr- 

 intendance, or whether the laying down of each kind of pavement is 

 confided to the particular persons whose interest it is to see that every 

 precaution necessary to ensure success be attended to. This latter 

 mode would seem not only the most natural, but the most desirable ; 

 for if each sort of pavement be not as perfect in its kind as it is possible 

 to make it, the comparison will not be a fair one. Nevertheless, from 

 what I have observed, it would appear really as if the persons directing 

 the laying down of the wooden pavement were exerting themselves in 

 behalf of their rivals, for never did I see work done in so slovenly and 

 insufficient a manner. I must, however, premise what I have further 

 to say by observing, that I am in no way whatever interested in the 

 question of the relative merits of the different kinds of pavement ; but 1 



am acquainted, well acquainted, with the nature of wooden pavements, 

 their advantages, and defects, and can affirm that no kind of pavement, 

 perhaps, requires to be constructed with greater care. 



1 . The hexagonal blocks must be cut with mathematical exactness 

 in all their dimensions. 



2. The surface on which they rest must be not only perfectly even, 

 but so solid and compact as not to be irregularly compressible into 

 hollows. The latter circumstance, indeed, is necessary to all pave- 

 ments. 



3. The blocks must be dry when laid down, else, if they be much 

 swollen by wet, they will contract considerably in drying, and the 

 pavement be no longer solid, but rickctty. When laid down dry, the 

 blocks will always be far enough from perfect contact to admit of such 

 slight swelling as may result from rain falling on their upper surface. 



4. The successive blocks of each successive range should be hard 

 rammed down to a level, determined by a transverse rule laid on them 

 from side to side, before another row is placed, so that if any block 

 sinks lower than another by being rammed, it may immediately be 

 lifted up, and fresh sand or fine gravel placed beneath it. 



5. The cross-section of a wooden pavement should have but very 

 little slope. 



Now, Sir, every one of these essentials to a good wooden pavement 

 is neglected in laying down the one in Oxford-street. 



1. The hexagons are very difterent in size. 



2. The surface on which they rest is one of a most irregularly- sized 

 gravel, a mixture of large and small rounded stones ; the very worst 

 bottom that could be chosen for the purpose. 



3. The blocks are quite wet when inserted. 



4. The blocks are not rammed as laid down. I believe they will 

 not be rammed till the space is all paved. 



.5. The cross section presents by far too great a convexity. The 

 different size of the blocks is such, that in many places the faces are 

 more than half an inch asunder, and the irregularity of the bottom on 

 which they rest will make them very ricketty. If, while wet, such 

 openings exist, what will there be in summer ? The ramming will be 

 done to make an even surface ; but unless each block be driven down 

 till it can go no further, the passage of carriages will soon make an 

 uneven road of it ; and if every block be rammed down to the utmost, 

 the whole pavement, with much labour, must be beat down to a level, 

 when any single block that may happen to go down lower than the rest. 



If well made, the surface of a wooden pavement is so smooth that 

 the slightest slope is sufficient to let the water run off. Too great a 

 slope is very dangerous on a wooden pavement ; for one of its incon- 

 veniences is its being exceedingly slippery in wet weather or in frosty 

 weather; indeed, this 1 take to be the great disadvantage of wooden 

 pavements for the streets of London (for court-yards, when well done, 

 it is excellent) ; many a poor horse's knees will suffer from it, and the 

 omnibus drivers, who already pull up their horses so suddenly that 

 they slide a few feet on the roughest stone pavement, will find it im- 

 possible to stop suddenly, but by the wheels striking against the 

 prostrate bodies of their cattle. 



It is found that the mud of our streets is produced from the squeezing 

 up of the subsoil. Now, this cannot possibly happen in a well-con- 

 structed wooden pavement, and such is, therefore, always free from 

 mud in winter, and from dust in summer, both very great advantages. 

 But the pavement, as laid down in Oxford-street, is so badly done, 

 that it will soon be covered with our slimy mud, and no horses' feet, 

 unless their shoes be made with iron spikes to them, will hold. Indeed 

 the thing is done in so hurried a manner that it cannot be good. A 

 clever workman cannot lay down more than two square fathoms of 

 wooden pavement in a day, supposing the soil beneath all ready to his 

 hand, and if the blocks are secured to each other by wooden pins, as is 

 found advantageous in some cases, he will not do more than 49 square 

 feet in a day. 



The necessity of a good bottom is such, that in some places it has 

 been found necessary first to lay down a good solid pavement, on 

 which a perfect floor of two inch planking is laid down, this is smeared 

 over with pitch, and finally, the hexagonal blocks are carefully placed 

 and secured each to the other with woodon pegs. This is, of course, 

 very expensive, and with us unnecessary, but a bard and perfectly 

 even bottom should be made before laying down the blocks. 



I could say a great deal more on the subject, having had opportu- 

 nities of studying it, not from motives of interest, but from a love of 

 information. I must, however, conclude this article, already, I fear, 

 too long. Any information in my power to give I will be happy to 

 communicate ; my address may be learned of Mr. Weale, Architectural 

 Library, Holborn. I am, Sir, your most obedient, 



27th December, 18.38. J. R- J- 



[The above communication was intended for our last Journal, but 

 was received too late for insertion. The wooden pavement in Oxford- 



