638 



NA TURE 



[October 25, 1906 



superelevation of 6-4 inches. The maximum super- 

 elevation on the South-Western Raihva)' is 6 inches, 

 and it is, of course, altogether impossible to work with 

 any such superelevation as more than 2 feet. It will 

 be understood that the whole of the constraining force 

 required to keep the engine moving in the curve is 

 supplied by the resolved component of the weight of 

 the engine acting parallel to the plane of the radius 

 towards the centre of curvature. 



It will be evident, therefore, that superelevation is 

 a rented}' of limited efficacy for a serious defect. The 

 centrifugal force at sixty miles per hour (a speed 

 that the evidence of figures shows to have been ex- 

 ceeded, but which we adopt as a convenient standard) 



would be ^ -, or, approximately, 24^ tons (24'597). 



32*2 X 520 



The accompanying diagram (Fig. i) illustrates the 

 resultant of the two opposing forces acting on the 

 engine. 



M = centre of gravity of the engine 5 feet above rail- 

 level. The line MQ = the weight of the engine, and 

 MF = the centrifugal force at sixty miles an hour to 

 the same scale. Completing the parallelogram 

 MFRQ, then MR = the resultant of the two forces. 

 Producing MR, it cuts the rail-level at the point H, 

 which is 5-29 inches inside the outer rail; AE is the 

 superelevation. There would only be, therefore. 



about 5 inches between the points A and H. The 

 narrowness of the margin of safety with the data 

 assumed is indicated very clearly in the diagram by 

 the nearness of H to A ; should H coincide with \, 

 the engine is just on the point of turning over. 

 The working out of the problem is as follows : — 

 Mr> = 54 tons. 

 M K = 24'596 tons. 

 MC = 6o inches. 

 AE = 3'5 inche.s. 

 AB = 56'5 inches. 

 MF 24i;g6 ,, „ 



'^"'■=MQ= 7/ =0-45548 

 (f = 24°29' 



AE 3-5 

 sine = sine r)= «>,= rfT.r = 0'o6i9 



fl = 3°33' 



9 = <p-B = 24° 29' -3° 33' = 20° 56' 

 CH = MC tan (>) := 60 X 0-383 = 23 (app. ) 

 AH = 28 25 - 23 = si inches. 



NO. 1930, VOL. 74] 



Working backwards with the same data, and 

 assuming the resultant to pass through A, it will be 

 found that the critical speed would be practically 

 sixty-six miles per hour. 



In order to calculate CH quickly and with an 

 approximation sufficient for practical purposes, the 

 above working mav be very much simplified by the 

 following formula, which has been suggested by Prof. 

 Dalby : — 



CH = /;( —!■ where ^ = superelevation in inches, 



G — the gauge in inches, V = lhe velocity in feet per second, 

 (■•=32'2, R = radius of curve in feet, /i=height of centre of 

 giavity of engine above the rail level in feet. 



The way in which the formula is obtained from 

 Fig. I is as follows : — 



o AE e 



^ = AB = G "PP- 



OR WV^ V^ 



«, = -'■ -i.W = — ^ very approximalely. 



Therefore 9 = 



approximately. 



Therefore CH = CM ■<{(!>- 8) = /it 



irR 



■i} 



The above gives a very nearly correct result when 

 the point H is in the neighbourhood of C, as it should 

 be. The error increases as H approaches A. 



We may compare the value of CH obtained by the 

 two methods ; we have already shown by the exact 

 inethod that CH=23 inches. Applying the approxi- 

 mate formula CH=23.6 inches. 



From the foregoing calculations it would appear 

 that if the train were travelling at a speed of more 

 than sixty-six miles an hour the engine would turn 

 over sideways, but it will be understood that deduc- 

 tions drawn in this way are not proof, though they 

 may be evidence, of what has occurred. The speed 

 of the train is, of course, a very indeterminate 

 quantity; the maximum superelevation was, as stated, 

 3I inches, but, to judge by the plan, this did not 

 extend on the curve for a greater distance than about 

 50 feet, and it would appear that at the spot where 

 the trouble commenced (to judge b}- the damage to 

 the line) the superelevation was somewhat less. 

 .\gain, in placing the position of the centre of 

 gravit)' of the engine, there are various unknown 

 factors which it would be necessary to take into con- 

 sideration to enable a true result to be reached ; for 

 instance, there is the unequal compression of the 

 springs causing lateral displacement of the centre of 

 gravitv, rush of water in the boiler, and the extent 

 of wear of wheels and rails. 



G. R. DUNELI.. 



ESTIMATION OF BLOOD-PRESSURE. 



THE subject of blood-pressure is one of great 

 interest both to the physiologist and the clinical 

 physician. By blood-pressure is meant the pressure 

 which the blood e.xerts on the interior of the heart 

 and blood-vessels, but it is chiefly with the vascular 

 blood-pressure — arterial, capillary, and venous — that 

 the physician deals. Our conception of intravascular 

 pressure is facilitated by considering what happens 

 wlien an aperture is made in an artery, capillary, or 

 vein of a living animal. In the case of the artery 

 the blood squirts out with considerable force, the 

 height of the jet measuring the pressure exerted on 

 the interior of the vessel. Experiment shows that the 

 pressure falls slowly from the heart to the region of 

 the smallest arteries, or arterioles, where there is a 

 considerable fall, the pressure in the capillaries and 



