1841.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



13 



face of the valve, it evidently acts on a greater surface, and which is 

 still greater tlie more the valve is raised." 



It is to the latter part only of this proposition that we object It is 

 clear that the eftective area of the valve must be augmented by its 

 being lifted from its seat, and, if it is only raised a very minute quan- 

 tity, merely suflicient to permit the escape of steam ronnd tlie edge, 

 the eftective area of the valve will be increased from that of its lower 

 to that of its upper surface; for in that case the steam, in passing 

 through between the valve and its seat, presses against the whole 

 conical surface of the former with sensibly the same pressure as exists 

 in the boiler ; but when the valve is raised considerably, as much for 

 instance as twice its thickness, the steam, in escaping round the edge 

 of the valve, will press on the conical surface of the latter with 

 diminished force in consequence of the rapid enlargement of the space 

 in which it is allowed to expand after having passed tlie lower surface 

 of the valve. This will be evident on referring to the annexed dia- 



gram, where efg h represents the valve -seat, and (i h c rf one-half of 

 the valve, in section, the rise a e being equal to twice the thickness 

 6 d. Now it is clear that the steam will pass upon the lower surface 

 cd o{ the valve a b, and on the conical surface e g of the seat with the 

 whole pressure in the boiler, but that, after passing the contracted 

 orifice e e round the valve, it will immediately expand very consider- 

 ably by reason of the rapid divergence of the surface a c and e/, and 

 will exert but a slight pressure on the conical surface a c of the valve. 

 But if the valve has only risen to the position a' b' c' d', (supposing 

 the rise a' c to be very small,) the aperture for the escape of the steam 

 becomes that represented by the line ek, at right angles to f if and a' c', 

 so that the effluent steam will exert its full pressure, not only against 

 the bottom siirface of the valve, but also against all its conical surface 

 from k I downwards. On the upper part a' k the pressure is but in- 

 considerable, as in the former case, so that the circle whose radius is 

 k I mav be looked upon as a near approximation to the effective area 

 of the valve : and it is obvious that this area is by so much the greater 

 as the rise of the valve is less, which is in direct opposition to the law- 

 laid down by M. de Pambour. We should express the law in general 

 terms thus : 



When the valve rests upon its seat, its effective area is equal to 

 that of its inferior surface, or rather of the orifice covered by the 

 valve : when the valve first begins to rise, its ertective area is equal to 

 that of its upper surface ; and, as it rises more and more, the effective 

 surface o-oes on diminishing, but according to a law which remains to 

 be determined. 



We therefore consider the calculation in pages 90 and 91 as falla- 

 cious. 



Before cjuitting the subject we shall just offer a remark on the para- 

 graph which closes this article, which is the following : 



"The above establishetl calculation, then, is to be depended on only 

 when the balance-screw can be lowered so as precisely to equilibrate 

 the interior pressure, as has been said above, without, however, allow- 

 ing the valve to rise. But the thing is not possible when the engine 

 produces a surplus of steam beyond what its cylinders can expand, be- 

 cause this steam must necessarily have an issue. In this case, then, 

 the pressure is to be found only by recurring afterwards to the baro- 

 meter-gauge, as we shall presently indicate." 



It seems the most natural hypothesis, that, the blowing of the valve 

 is a sign that more steam is generated in the boiler than can be ex- 

 pended in the cylinder ifMout raising the pressure in the boiler, and 

 that the blowing may always be prevented by a suitable augmentation 

 of the weight on the valve. 



The second article, which completes this chapter, contains a full 

 description of the four instruments employed by the author to deter- 

 mine the pressure of the steam, with an explanation of the mode of 

 using them, namely, the barometer-gauge, the air-gange, the thermo- 

 meter-gauge, and the spring-gauge or indicator. 



The fourth chapter treats of the Resistance of the Air, and we are 

 sorry to find this subject not so fully elucidated as we had hoped. 



The apparently anomalous result observed b\- Borda, and confirmed 

 by M. Thibault, namely, that large surfaces experience a greater re- 

 sistance from the air in proportion to their area than smaller ones, 

 when submitted to a circular motion round an axis situated in the 



same plane as the given surface, was easy to foresee. But, as M. de 

 Pambour has neglected to give the explanation of it, we shall do so, 

 in order that those, to whom the true reason may not occur, may not 

 reject the proposition as absurd. The explanation will be found in 

 the following calculation. 



Let a square surface whose side =: a revolve round an axis, situated 

 in the same plane as the given surface and at a distance )• from its cen- 

 tre. Let the velocity of the centre ^: v, and let p = the resistance of 

 the air against an unit of surface moving at the unit of velocity, and 

 R the resistance on the whole given surface. The resistance on an 

 element of the surface extending across its whole width, and at a dis- 

 tance .r from the axis of rotation will be 



d.R: 



a p V- 



x- d. X ; 



vhence we obtain by integration 



and, putting for .r its maximum and minimum values, namely, c-l-- 

 and )• — ' we have, fur the resistance on the whole given surface, 



^=^"C('+0"('-0' 



R: 



The resistance on an unit of area will be found by dividing the total 

 resistance R by the area of the surface, which is a". We have there- 

 fore, calhng TT the mean resistance per unit of area under the above 

 circumstances. 



^(-'+0^ 



-.pr- 



The terra shews that the above quantity increases with the 



12 ;•'-■ 



ratio of the area of the surface to the square of the distance of the 

 centre of the surface from the axis of rotation, so that, if this distance 

 is constant the resistance per unit of area is greater for a large surface 

 than for a smaller one, and that the same effect is produced by lessen- 

 ing the distance from the axis of rotation to the centre of the surface. 



It is essential, therefore, as the author observes, that, when the cir- 

 cular motion is used to determine the resistance of the air, that the 

 surfaces employed should be of very small extent compared to the 

 length of the radius of rotation. 



The following formula, to determine the resistance experienced by a 

 body moving in the air at rest, is deduced from the experiments of 

 Borda, Dubuat and M. Thibault. 



Q = -0011S9G 6 2 V-, 

 in which Q is the total resistance in lbs., V the velocity of feet per 

 second, 2 the front surface of the body, traversing the air in a direction 

 normal to that surface, and c a coefficient which varies with the length 

 of the body. 



In applying this formula we must make 



for a thin surface - - - - - -e^ 1'43 



for a cube - - e^l"17 



for a prism of a length equal to 3 times the side of 



its front surface ------ 6z:;l-10. 



In the and section the author has given a table of G experiments on 

 the resistance of the air against trains. Five wagons of different 

 heights, loaded with goods, were drawn to the top of the Whiston in- 

 cliiied plane on the Liverpool and Manchester Railway, and were 

 allowed to descend by their own weight, first separately, and after- 

 wards all united in one train. 



The comprehension of this table would have been greatly facilitated 

 if the author had given some fuller explauations of the manner in 

 which he determined the last number in the 8th column, expressing 

 the effective surface exposed to the shock of the air, which gives, for 

 the five w-agons together, a friction equal to the sum of the frictions of 

 the five wagons separate. We have worked out the formula given in 

 page 152 with different areas of effective surface, and find the friction 

 amount to 5-92 lb. per ton with 144 square feet, and not 130, as given 

 by M. de Pambour. The surface of the highest wagon, augmented by 

 that representing the resistance of the wheels and screened parts of 

 all the five wagons, is equal to 127 square feet, and as we have found 



