44 



NATURE 



[May 8, 1890 



A Fresh Sample. 



January 28 

 .. 28 



0*63 

 I -06 



1-28 

 2-14 



Barely perceptible. 

 Just enough. 



For convenience of comparison they are arranged, not in order 

 of date, but in order of densities of film. 



The sharpest test of the quantity of oil appeared to occur 

 when the motions were nearly, but not quite, stopped. There 

 may be some little uncertainty as to the precise standard indi- 

 cated by "nearly enough," and it may have varied slightly upon 

 different occasions. But the results are quite distinct, and under 

 the circumstances very accordant. The thickness of oil required 

 to take the life out of the camphor movements lies between one 

 and two millionths of a millimetre, and may be estimated with 

 some precision at i "6 micro-millimetre. Preliminary results from 

 a water surface of less area are quite in harmony. 



For purposes of comparison it will be interesting to note that 

 the thickness of the black parts of soap films was found by 

 Messrs. Reinold and Riicker to be 12 micro-millimetres. 



An important question presents itself as to how far these water 

 surfaces may be supposed to have been clean to begin with. I 

 believe that all ordinary water surfaces are sensibly contamin- 

 ated ; but the agreement of the results in the table seems to 

 render it probable that the initial film was not comparable with 

 that purposely contributed. Indeed, the difficulties of the 

 experiments proved to be less than had been expected. Even 

 a twenty-four hours' exposure to the air of the laboratory ^ does 

 not usually render a water surface unfit to exhibit the camphor 

 movements. 



The thickness of the oil films here investigated is, of course, 

 much below the range of the forces of cohesion ; and thus the 

 tension of the oily surface may be expected to differ from that 

 due to a complete film, and obtained by stddition of the tensions 

 of a water-oil surface and of an oil-air surface. The precise 

 determination of the tension of oily surfaces is not an easy 

 matter. A capillary tube is hardly available, as there would be 

 no security that the degree of contamination within the tube was 

 the same as outside. Better results may be obtained from the 

 rise of liquid between two parallel plates. Two such plates of 

 glass, separated at the corners by thin sheet metal, and pressed 

 together near the centre, dipped into the bath. In one experi- 

 ment of this kind the height of the water when clean was 

 measufed by 62. When a small quantity of oil, about sufficient 

 to stop the camphor motions, was communicated to the surface 

 of the water, it spread also over the surface included between 

 the plates, and the height was depressed to 48. Further 

 additions of oil, even in considerable quantity, only depressed 

 the level to 38. 1 .?> .^ f 



The effect of a small quantity of oleate of soda is much 

 greater. By this agent the height was depressed to 24, which 

 shows that the tension of a surface of soapy water is much less 

 than the combined tensions of a water-oil and of an oil-air sur- 

 face. According to Quincke, these latter tensions are respec- 

 tively 2-1 and 3-8, giving by addition, 5-9 ; that of a water-air 

 surface being 8*3. When soapy water is substituted for clean, 

 the last number certainly falls to less than half its value, and 

 therefore much below 5 -9. 



April 24. — "On a Pneumatic Analogue of the Wheatstone 

 Bridge. By W. N. Shaw, M.A., Lecturer in Physics in the 

 University of Cambridge. Communicated by Lord Ravleigh, 

 Sec. R.S. / s > 



When fluid flows steadily through an orifice in a thin plate, 

 the relation between the rate of flow, V, measured in units of 

 v.dume of fluid per second, and the head H (the work done on 

 unit mass of the fluid during its passage) may be expressed by 

 the equation : — ' j tr } 



H = RV2, 



where R is a constant depending upon the area of the orifice. 

 , z! 9 , ^^ measured in gravitation units, R is equal to 

 \l2gk a\ whereto- IS the acceleration of gravity, a the area of the 

 orihce, and /& the coefficient of contraction of the vein of fluid, a 

 factor which is independent of the rate of flow. 



Measurements made upon the flow of air in o'rder to determine 

 the coefficient of contraction have been hitherto such as may be 



' In the country. 



termed "absolute" ; that is to say, the head and the flow hav 

 each been separately expressed in absolute measure and the valu 

 of R determined by taking the ratio of the head to the square . 

 the flow. This process is exactly analogous to measuring th 

 electrical resistance of a wire by finding the electromotive fore 

 between its ends and the current which flows along it. 



M. Murgue, in a work on "The Theory and Practice of Cen- 

 trifugal Ventilating Machines" (translated by A. L. Steavenson), 

 has shown that the internal resistance of a centrifugal fan to the 

 flow of air through it can be calculated from the effects produced 

 on the flow by varying the size of a second orifice through which 

 the air had to pass. This process is evidently parallel to calcu- 

 lating the internal resistance of a battery by finding the effect 

 produced upon the current by varying the external resistance. 

 The further development of the analogy seems to afford a "null " 

 method of comparing resistances to the motion of air, and 

 of verifying the laws of flow, and one which requires only a 

 detector and not an anemometer, and is independent of the 

 constancy of the flow. Whether it could be used practically to 

 test the laws of flow and measure the pneumatic constants for 

 various orifices to a higher degree of accuracy than has hitherto 

 been attained, evidently depends upon the sensitiveness of the 

 arrangement. In order to try this, the author constructed what 

 may be called a pneumatic analogue of the Wheatstone Bridge. 

 It consists of three wooden rectangular boxes. A, Bj, B.,. 

 The ends of Bj and B^ abut against the side of A ; between 

 Bi and A is a rectangular opening, a^_, i in. x J in., in a card- 

 board diaphragm ; between Bg and A a rectangufar operting, a^, 

 I in. X I in., in a similar diaphragm. In the side of Bj at a^ is 

 an adjustable slit, made by cardboard shutters sliding in card- 

 board grooves, and at a.^ in the side of Bg, opposite to a^, is a 

 similar adjustable slit. The tube connecting Bj and Bg, or 

 "galvanometer" tube, is a straight tube of glass, G, of about 

 I -I inch internal diameter. It can be closed at one end by a 

 small trap-door in the interior of the box Bj, which can be 

 opened and shut by a steel wire passing through a cork in 

 the top of Bj. The sensitiveness of the apparatus depends upon 

 the indicator employed. There are many indicators that might 

 be suggested ; the one tried and found to work well consists of 

 two very small parallel magnetized sewing needles, stuck through 

 a cap of elder-pith, supported on a small agate compass centre ; 

 the needles carry very light mica vanes on one side of the centre, 

 counterpoised by a small quantity of platinum wire. The whole 

 is balanced on the point of the finest needle obtainable, and 

 forms a very delicate wind vane. The needles take up a 

 definite position of equilibrium with the planes of the vanes 

 approximately north and south. The apparatus being so placed 

 that the tube, G, is east and west, the vanes always set across 

 the tube when there is no current. The needle-points enable 

 the position of equilibrium to be clearly identified by the aid of 

 a fiducial mark r n the glass tube. The sensitiveness can be 

 altered as desired by an external control magnet, just as that of 

 a galvanometer needle can be. The little compass needle or 

 wind vane, M, is very sensitive to the motion of air in the tube. 

 The head is produced by a gas-burner in a metal chimney 

 fitted to the lid of the box A. 



Of the four apertures of the bridge, two, viz. a^ and a^, are 

 inaccessible without pulling the arrangement to pieces ; they 

 represent areas of | sq. in. and i sq. in. respectively, as 

 accurately as a knife can cut them in cardboard. 



The other two areas, viz. a-^ and Cg, are made by sliding 

 shutters, as already mentioned. The edges were cut with a knife, 

 and they probably are only rough approximations to areas in a 

 truly thin plate. 



If the coefficient of contraction may be assumed to be in- 

 dependent of the shape of the orifice, we get the condition for 

 no flow through the "galvanometer " tube : — 



where the d% represent the actual measured areas of the four 



orifices. 



Observations have been taken with the apparatus — 

 (i) To verify the law of proportionality of areas, viz. 



(2) To verify the inference that the condition of no flow is 

 independent of the total head. 



