1846.J 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



37, 



discoveries which we have analysed, and particularly from the admirable 

 ■works of the bridge of Soiiillac. Engineers, to their honour, never refuse 

 to assign a large share to M. Vicat of the success which they obtain, even 

 when circumstances permit them to have recourse exclusively to natural 

 hydraulic lime, and natural pozzolanas. Thus, for example, on the occa- 

 sion of the entirely successful completion of the new basin for repairing 

 vessels at Toulon, founded 42 feet above the level of the sea, the able 

 director of these works, M. Noel, wrote on the 24tli of April last to the 

 Under Secretary to the Department of Public Works ; "At a time when 

 the law respecting M. Vicat is about to be discussed, it will not be super- 

 fluous to bring to your knowledge a fact which gives a new importance to 

 the labours of the illustrious engineer who lias done so much for the ad- 

 vancement of our art." 



Thanks to the laborious and patient researches of M. Vicat, works 

 once deemed impossible, are executed at the present day safely in every 

 part of the kingdom, and without requiring enormous expenses. 



We will not repeat the numerical computations already given respecting 

 the economy efl'ected in public works by M. Vicat's invention. Those 

 computations should be retained in every mind. It would, in fact, be dif- 

 ficult to cite a discovery which, in t!ie short interval of 26 years, has pro- 

 duced such colossal and useful results. 



The Commission are unanimously of opinion, that in voting, without 

 some modification, the law which has been proposed by the Minister of 

 Public Works the justice rendered to M. Vicat would not be complete. 

 They would desire that the pension of 0,000 francs should be accorded 

 more explicitly under the title of a i^'ational Rt'compctise. This is the only 

 change of which the Government proposition appears to us susceptible. 

 We trust that the Ciiancellor, adopting our opinions respecting the services 

 rendered to the country by JI. Vicat, will assent to the amendment which 

 we have the honour of suggesting, and which has already received the 

 sanction of the iNIinister of Public Works. 



ATMOSPHERIC TRACTION. 



Sir — Since the appearance of Mr. Haydon's paper in your November 

 Part, I have been inclined to pay some attention to the atmospheric sys- 

 tem. The favourable results actually obtained after so few attempts led 

 me to expect some error in the numerical example appended to the fore- 

 mentioned paper, especially when the length of the formula and the diffi- 

 culty of substitution were taken into account. I made several attempts 

 with the formula as it now stands, but in every case arrived at different 

 results, and each of them at variance with that deduced from the work 

 done each stroke. One source of error seems to have arisen from taking 



!0.)390(J n 



R = 99, instead of its exact value ^^^ for if R =^ we get n = lll or 



87, nearly according as the former or latter is used. I was surprised at the 

 difference in the results, but it teaches us how careful we ought to be to 

 ensure approximations in our results. In my application to the example 

 at Dalkey, I shall suppose the whole length of the connecting pipe to be 

 used for propelling the train, as local circumstances compelled them in 

 that instance, to place the engine at an inconvenient and extravagant dis- 

 tance from the main tube. 



Let u„ denote the work done during the nth stroke of the air pump. 

 W^ denote the work done at the end of the nth stroke. 

 ^^' n '^'^""''^ ^^'' '"''"''' '^""'^ during the motion of the train, their hav- 

 ing been n strokes of the air pump before the train started. 

 W, the useful effect communicated to the tube piston. 

 Then it is found by Mr. Haydon, that 



Wn =I5afcR"~^(l-^rrilog,R + ^Z:i log -^ 1 

 fl R" X S A X 







Where R = 



B-hC 



(1-R) = 1-- 



A + B + O 



B + C 



r, andA + B + C = S 



_A. 



S-A 

 S 



K, 



log R 



after the proper substitutions have beea made. 



(A) 



The correctness of the simplification may be tested in the following man- 

 ner : W|j — Wj|— I rework done at the nth stroke— that done at the end of 

 the n-l'h- 



15 a ic 



■d-R" 



+ U nlog R-(l- 



- R + n - 



1r" 'log p.) I 



liak(„n~l nil / ,„n— I ,.n, n — 1\, „) 



=-_-^|R -R+^-hCR -R ) +R I'oSe^j 



= 15 « A: r"-^ / 1 + (i^r") '""^ " } 



= 15 a fc r"~ 1 1 + ( « ) 'ogj R I =W =work done during the 



nth stroke. Let n have such a value that R„ = J '" then n=;S7 nearly. 



W« 



15 a 7c f , , , ) 



= — j^l 2 — (1-098612) j =5afc_(-90138771) 



= 720 S X 90 1 3877 1 lb. raised one foot. 

 Where S = vol. of the tube and air-pump cylinder expressed in feet. 

 Wg, =720x 10673-74X -90131771 = 6,927,242. 

 W-8,=5 X 176-7 X 8588 = 8,335,720. 

 W = 10 X 176-7 X 8588 = 15,174,926. 

 Wj, +W'g, = 15,274,926 = work done. 



W = 15,174,996 = useful effect of work done. 



Subtracting, 87,972 = loss. 

 Hence the loss is about y},-, of the power given out by the engine. 

 Let B-|-C=V = vol. of lube to be exhausted ; w = vol. of air-pump cylin- 

 der; S =: V 4- V. 



^„ = li^Jl_R«,R'.,0,^R»} 



W. 



= 15afc(.Il^(l-R%R"log R"l 

 = 2160 (V + f) f l-R" + R"log, R| 



Where V and i- are expressed in cubical feet. 



W'„=2100 R" V loge — = -2160 r" V log 

 R" 



W = 2160 V(l-R") 



W 



„ + W'„ = 2160(1-R" + 2160d | i_R« + R" log^ R" | 



.-. Loss = 21G0xt> ■[l-R''-t-R"logeR"| 



For the loss in the Dalkey line we have = 2160 x 134-65 x \ (-90138771) = 

 720 X 134-65 x -90138771 = 87,387 lb. raised one foot high. 



This agrees very nearly with the former result, and therefore we may 

 suppose that the necessary loss is correctly determined. 



This we see varies as the volume of the air-pump. If W^^ be a maximum 



= 



li n 



= R"-llog^R(l+ (^^-") log«K)-l^ 



n-1 



Jog 



R, orO=- — n, 



K= — = 79 nearly. 

 A 



R'3 = 11 nearly, which agrees with Mr. Stephenson's experiments. 



It may be observed that the above formula; are true, for positive inte- 

 gral values of «. By examining the diagrams which accompany the Re- 

 port to the Directors of the Chester and Holyhead Railway, it will be 

 found that the pressure of the air in tlie pump became equal to the pres- 

 sure of the atmosphere sooner than we should have expected from theory. 

 This would no doubt be caused in some measure by the heat developed 

 during compression, but before the stroke commenced, the pressure in the 

 pump cylinders generally exceeded that in the branch pipe — so that pro- 

 bably more air rushed into the pump each time than was sufficient to re- 



