1S49.] 



THE CIVIL ENGINEER ANP ARCHITECT'S JOURNAL. 



35 



to centrifiigal force in a ring revolving uniformly. The te.mwn fin 

 pounds) = the weight of the ring (in pounds) X by its length (in 

 feet) -^ htf 32^ times the square of the number of seconds in which 

 the ring revolves. 



We shall next examine the effect of a progressive motion com- 

 bined with tlie rotation of the ring, and proceed to show that if 

 the centre of the ring have a progressive motion, the tension will 

 be the same as if the centre were fixed. This may be easily seen 

 from the following illustrations. Suppose that in a ship or car- 

 riage moving with uniform rectilineal motion, a string with a 

 weight at one end of it were whirled rai)idly, — it is quite clear 

 that the tension of the string would not be at all influenced by 

 the progression of the carriage or vessel ; the centrifugal force 

 would be the same, whether the plane of the string's rotation were 

 horizontal or vertical — parallel or perpendicular, to the direction 

 of progression. Again, a hoop rolled along smooth ground with 

 an assigned velocity, whether it be directed eastward or south- 

 ward, or to any other point of the compass — that is, whether its 

 progressive motion coincide with or be inclined to the course of 

 the earth's diurnal rotation. So also, a body resting at any point 

 on the earth's surface, except its poles, suffers a diminution of 

 weight on account of the centrifugal force arising from rotation 

 about the earth's axis ; but this diminution is not at all influenced 

 by the annual or progressive motion : the centrifugal force is also 

 the same for every hour of the day, and on every day of the year — 

 that is, for every angle at which the diurnal motion at the point in 

 question can be inclined to the earth's orbit. 



We see then that the centrifugal force of a body rotating in a 

 circle about an assigned centre, is measured, not by the absolute 

 motion, but by the rotation relatively to that centre. Consequently, 

 the rule above given for determining the tension of a ring revolv- 

 ing about a fixed centre, applies to the tyres of railway wheels, 

 which have not only a circular motion about their axles, but a uni- 

 form progressive motion also. 



It may, however, be more convenient to transform the rule, so 

 as to express the tension of the tyre in terms of the velocity of 



"Wl 



the train. We have shown that T = — ;, where / is the length of 



the circumference, and t the time of revolution. Now, if the 

 wheel do not slip, the train moves through a distance / during the 



time t ; therefore, if V be the velocity of the train, V := , and 



the above expression becomes T 



WV^ 



~7^ 



Let K be the sectional 



area of the tyre, and t the tension per unit of area; T = tk. Also, 

 it is evident that the solid content of the ring may be put equal to 

 its length multiplied by its sectional area (= Ik). Hence, if the 

 weight of a unit of volume be w, we have W = wtic. Substituting 

 then for W and T, 



TK = U)«— ; or, T = . 



9 g 



Now, this expression, if we take a foot for the unit of length, 

 gives the tension per square foot of the metal ; but what is usually 

 required is the tension per square inch, which is of course the 

 ] 44th part of the tension per square foot. Hence the following 

 very simple rule, since \Ug = 144 X 32^ = 4637 : — 



The tension of the tyre in pounds per square inch due to centrifugal 

 force equals the 4637 th part of the weight in pounds of a cubic foot of 

 the metal multiplied by the square of the number of feet which the train 

 travels in a second. 



The facility of applying this rule depends materially on its in- 

 dependence of the rad'ius and other dimensions of the" tyre. As 

 the weight of a cubic foot of iron or steel varies from about 4,600 

 to 4,800 lb., the following rule is sufficiently accurate for i)ractical 

 purposes : — 



The tension in pounds on every square inch of the sectional 

 area of the tyre ^ the square op the nu-mber of peet which the 



TRAIN TRAVELS IN A SECOND. 



For example, if the train moved 85 feet per second (a mile per 

 minute), the strain on the metal per square inch would be 7223 lb. 

 = 3-23 tons. It is curious to observe, that in the same train every 

 tyre would be subject to the same degree of strain, whatever its 

 radius, width, and thickness. 



SUBMARINE FOUNDATIONS. 



On Submarine Foundations; particularly the Screw-Pile and Moor- 

 ings. By Alexander Mitchell, M. Inst. C.E. — (Paper read at 

 the Institution of Civil Engineers.)* 



The entire subject of the methods of preparing submarine foun- 

 dations, if treated of in as general and comprehensive a manner 

 as its importance demands, would not only far exceed the limits 

 of a paper for the Institution of Civil Engineers, but would be 

 tedious and unnecessary, as the majority of the members are tho- 

 roughly conversant with the various systems in their daily prac- 

 tice ; it is proposed, therefore, to limit the present inquiry to a 

 cursory mention of the ordinary methods, and to devote the greater 

 space to a description of the Screw Pile and the Screw Mooring, 

 and of the works in which they have been employed. Sheet piling, 

 whether of wood, or iron, is now familiar to every one, as the 

 driving it is an operation of daily occurrence, and the numerous 

 scientific treatises on stone foundations, placed in positions of pe- 

 culiar difficulty and danger, render all comment upon them quite 

 superfluous. 



The Eddystone and Bell Rock Lighthouses furnish splendid ex- 

 amples of such works. The scientific skill employed in joining 

 and binding together their parts, giving to them almost a mono- 

 lythic solidity and strength, is beyond all praise; and yet were 

 lighthouses now required to be placed in similarly exposed posi- 

 tions, it is more than probable that strong open-work structures, 

 upon iron piles, would be substituted for solid stone towers, as a 

 vast saving would thus be effected, and the strength would be in- 

 creased by removing the only cause of danger ; for the waves are 

 only formidable when they are inflexibly opposed. In that part of 

 the subject which relates to foundations placed in banks of loose 

 sand or mud, covered by the sea, the author would confine his ob- 

 servations to his own practical experience, and studiously avoid all 

 comi)arison with other modes of proceeding, which he is aware 

 may, and probably will, be brought before the Institution, and will 

 doubtless receive the usual impartial consideration. 



An account of the circumstances which led to the introduction 

 of the screw-pile and screw-mooring, would possess but little gene- 

 ral interest, and is not necessary. It will suffice to observe, that 

 a project, contemplated by the author, involved the necessity of a 

 much greater holding power than was possessed by any pile or 

 mooring then in use ; the former being nothing more than a 

 pointed stake of considerable size, easily either driven into or ex- 

 tracted from the ground, and the latter a large mass of stone or 

 iron, which when submerged became of limited power, and was 

 quite incapable of resisting an upward strain. 



The plan which ap- *''B- '• 



peared best adapted for 

 obtaining a firm hold of 

 soft ground or sand, 

 was to insert to a con- 

 siderable distance be- 

 neath the surface, a bar 

 of iron (fig. 1.) having 

 at its lower extremity 

 a broad plate, or disc of 

 metal, in a spiral or 

 helical form, on the 

 principle of the screw, 

 in order that it should 

 enter the ground with 

 facility, thrusting aside 

 any obstacles to its de- 

 scent, without materi- 

 ally disturbing tne tex- 

 ture of the strata it 

 passed through, and that it should at the same time offer an ex- 

 tended base, either for resisting downward pressure, or an upward 

 strain. Whether this broad spiral flange, or "Ground Screw, ' as it 

 may be termed, be applied to the foot of a pile to support a super- 

 incumbent weight, or be employed as a mooring to resist an 

 upward strain, its holding power entirely depends upon the area of 

 its disc, the nature of the ground into which it is inserted, and the 

 depth to which it is forced beneath the surface. The proper area 

 of the screw should, in every case, be determined by the nature of 

 the ground in which it is to be placed, and which must be ascer- 

 tained by previous experiment. The largest size hitherto used 

 has been 4 feet in diameter ; but within certain sizes, prescribed 

 by the facility of manufacturing them, the dimensions may be ex- 



* An abstract of this paper was gireo io the Jouroa], Vol. XI. C1B48}, p. t2. 



6* 



