ii6 



NA TURE 



[June i, 1893 



pose of determining [he thickness of black soap films formed of 

 solutions of varying composition. Two methods of experiment 

 were employed: (l) an optical method, in which the mean 

 thickness of about 50 plane black films contained in a tube was 

 deduced from observations of interference phenomena ; and (2) 

 an electrical method, in which the thickness of a cylindrical 

 black film was derived from a measurement of its electrical 

 resistance. The optical method involves the assumption that 

 the refractive index of a thin film of liquid is the same as that of 

 a large quantity of the same liquid. 



Reasons are given for the belief that the refractive indices in 

 question, if not identical, differ only slightly, and hence that the 

 thickness of a film as determined by the optical method is the 

 true thickness. 



In the electrical method the assumption is made that the 

 specific conductivity of a liquid does not alter when the liquid 

 is drawn out into a thin film. 



If the results obtained by the two methods agree, the con- 

 clusion is that the specific resistance of a film is not aflfected by 

 its tenuity ; if they differ widely from each other, a change in 

 the specific conductivity of the liquid must have taken place. 



The authors showed, in 1 883, that for a solution of hard soap 

 containing 3 per cent, of KNO3, with or without the admixture 

 of glycerine, the mean thicknesses of black films, as measured 

 by each of the two methods, were in close agreement. For 

 such solutions, then, the specific conductivity is the same 

 whether the liquid be examined in considerable bulk or in the 

 form of a film 1 2jn/n in thickness. The accuracy of this result 

 has been confirmed by a large number of observations made 

 during the last three years. 



If the proportion of KNO^ added to the solution be dimi- 

 nished, the thickness of a black film, whether measured optically 

 or electrically, is found to undergo a change. 



The results obtained by the optical method show that 



(1) For a given solution of hard soap the thickness of a black 

 film increases as the percentage of KNOj is diminished, being 

 I2'4(u^ for a 3 per cent, solution, and 22'i for a solution 

 containing no salt. This is confirmed by experiments on soft 

 soap. 



(2) When no metallic salt is dissolved in the solution the 

 thickness of a black film increases as the strength of the soap 

 solution diminishes. The thicknesses are 21 •6, 22'i, 277, and 

 29'3,u,u when the proportions of soap to water are respectively 

 1/30, 1/40, 1/60, I /So. 



(3) If the solution contain 3 per cent, of KNO3, variation in 

 the proportion of soap dissolved produces very little change in 

 the thickness of a black film. 



Electrical Melhod. — -It has been stated that for a soap solu- 

 tion containing 3 per cent, of KNO3 the thickness of a black 

 film as measured electrically is practically the same as that 

 measured optically. If, however, the proportion of KNO3 be 

 diminished, the thickness (measured electrically) increased in a 

 far larger ratio than would be inferred from the optical method. 

 If the proportion of salt be diminished to zero, the thicknesses 

 ■ thu5 calculated are much greater than the greatest thickness at 

 which a film can appear black. In such cases, therefore, the 

 electrical method does not give the true thickness of the black, 

 and the hypothesis that the specific conductivity of the film and 

 of the liquid in mass are identical is untenable. 



The following table shows the change in apparent thickness 

 due to diminution in the quantity of dissolved salt : — 



Hard Soap. 

 Percentage of KNO5. 321 0*5 q 



Mean apparent thickness ofj 

 black film (measured elec- ,-io'6 ... la'; ... 24*4 ... -zb's ... 154 

 trically) J 



The large value obtained for the apparent thickness in the 

 case of the unsalted hard soap solution is confirmed by experi- 

 ments on a solution of unsalted soft soap, which gave a mean 

 apparent thickness of 162/1^. 



In dilTerent films the measured thicknesses of the black differ 

 widely from each other, the limits being roughly S^^u^ and 

 230^,11. This large variation is due in some cases, at all 

 events, to a real variation in the thickness. Two different 

 shades of black are (incases where the solution contains little 

 or no salt) frequently seen in a film. They are separated from 

 each other by a line of discontinuity which is irregular in shape. 

 Comparative measurements on the two shades of black have 

 been made, and the results indicate that the electrical thick- 



nesses of the two kinds of black are approximately as 2 : i. 



The results of numerous experiments carried out with the 

 object of determining the cause of the great increase in electrical 

 conductivity in black films made from unsalted soap solutions 

 have shown that the increase of specific conductivity in ques- 

 tion — 



(i) Is independent of moderate changes of temperature. 



(2) Is not due to the absorption or evaporation of water by 

 the film. 



(3) Is not due to change in the composition of the liquid by 

 electrolytic decomposition produced by the current used to 

 measure the electrical resistance of the film. 



(4) Is not affected by a very large change in the quantity of 

 COo in the air around the film. 



(5) Is practically unaltered if the films are formed in an at- 

 mosphere of oxygen. 



The next question to be answered was whether the large 

 changes in specific conductivity affect black films only, or 

 whether similar phenomena can be detected in the case of 

 thicker films. 



The conclusions arrived at were (i) that the specific con- 

 ductivity of a film increases as the thickness decreases, and 

 (2) that this increase is less in the case of a film to which a salt 

 has been added and is nil when the proportion of salt is as 

 much as 3 per cent. 



The paper concludes with a discussion as to the cause of the 

 increase of electrical conductivity in thin films. The authors 

 point out that it may be attributed either to a modification of 

 the chemical constitution of the film brought about by its 

 tenuity, or to the formation of a pellicle on the surface or to 

 both causes combined. 



Physical Society, May 12.— -Prof. A. W. Riicker, F.R.S., 

 President, in the chair. — A paper on the drawing of curves by 

 their curvature, byC. V. Boys, F. R.S., was read, and demonstra- 

 tions of the melhod employed given. Whilst giving a course of 

 lectures on capillarity, in 1891, the author wished to explain the 

 principles upon which the form of a water drop depended, 

 and finding Lord Kelvin's rule (Proc. A'. Inst., Jan. 29, 

 1886) cumber.'iome, devised the modification now described. 

 The construction depends on the fact that the total curva- 

 ture is proportional to the hydrostatic pressure, i.e., pro- 

 portional to the depth below the plane sur/ace of the liquid. 

 To avoid the trouble of finding reciprocals, a rule was divided 

 so that the distance from what would be the zero cf the 

 scale are the reciprocals of the numbers attached to them, and 

 the curvature of an arc, being the reciprocal of its radius, 

 can be read oft" immediately by the rule. To meet cases where 

 the curvatures of surfaces are, in opposite directions, the zero, 

 or <», is put at the middle of the rule and divided both ways. 

 The chief gain depends on the abolition of cumulative errors 

 due to compass settings, which is effected as follows : The rule 

 is made of a thin slip of transparent celluloid with a small 

 hole at the centre or 00. A small brass tripod with needle feet 

 is placed so that two feet just penetrate the paper and the 

 third rests on the longitudinal straight line of the strip, which 

 passes through the centre hole, thus forming a temporary but 

 rigid centre about which the rule can rotate. A pen or pencil 

 through the hole at c» traces out an arc whose curvature is equal 

 to the reading of the scale where the needle point presses. 

 When the rule crosses the axis of rotation of a generating 

 curve, the numbers representing both curvatures are visible, 

 and the position of the needle-point corresponding to a given 

 total curvature can readily be found. A small arc is then 

 drawn. Holding the strip firmly on the paper, the tripod is 

 moved a little so that the sum of the two readings at the needle 

 point and where the rule crosses the axis has the value corre- 

 sponding to the position of the tracing point, and another arc 

 drawn. Repeating the process, a very perfect and accurate curve 

 results. Details for drawing nodoids, unduloids, catenoids, and 

 other curves are given in the paper, and many beautiful examples, 

 which had been executed bylVIiss Stevenson, were exhibited at the 

 meeting. The author also pointed out that the locus of points 

 about which the strip successively turns is the evolute of the 

 curve drawn by the tracing point. Prof. Perry considered the 

 method a new departure of great value. When he (Prof. Perry) 

 drew the capillary surfaces of revolution in 1875, he found that 

 cumulative errors produced considerable discrepancies. Prot 

 Greenhill said one would now be able to secure better diagrams 

 of transcendental and other curves than heretofore, and he 



NO 1231, VOL. 48] 



