66 



NATURE 



[July 13, 191 1 



of the pipe and the velocity oi flow. this ratio lias been 

 called by Osborne Reynolds " mechanical viscosity," to 

 distinguish it from the corresponding ratio when the field 

 is in steady or laminar motion, which is the ordinary 

 coefficient of viscosity. The fluid chosen for the purpose 

 of the experiments was air flowing at speeds up to 

 2200 cm. per second through pipes 508 and 7-35 cm. 

 diameter. A small Pitot tube of width 025 mm., con- 

 nected to a very sensitive gauge reading to 0005 mm. of 

 1 ater, has been used for measuring the distribution of 

 velocity, and a second sensitive gauge has been used for 

 measuring the shearing forces. The results of the experi- 

 ments are as follows : — (1) In pipes artificially roughened 

 so that air friction varied as square of velocity of flow, 

 the value of n' was found to be proportional to the pro- 

 duct of speed of flow v .. and linear dimension of pipe I, 



i.e. I- =kvj — where 7; is a constant depending on the 

 roughness. (2) In ordinary smooth pipes the correspond- 

 ing relation was given by F = Ci/</ f{ — ]— wheie C is a 



constant and 



/Q 



a function of the kinematical co- 



effii ient of viscosity V and the above product v c l. (3) In 

 ordinary smooth pipes of different diameters, owing to the 

 existence of a region of viscous flow at the boundaries, 

 exact similarity between the distributions of axial velocity 

 from centre to walls only obtains when the two viscosities 

 (p. and p.') are the same for each pipe. — Dr. G. W. C. 

 Kayo : A silica standard of length. The general proper- 

 ties of fused silica, and in particular its remarkably low 

 coefficient of expansion, render this substance specially 

 suitable for the construction of permanent length-standards 

 of the highest class. The coefficient of expansion of 

 platinum-iridium, which has hitherto been the material 

 almost exclusively employed in the best work, is about 

 9x10-' per degree C, while that of silica over the 

 ordinary range is about 0-4x10-', i.e. one-twentieth of this 

 amount. It is true that the best qualities of invar — M. 

 Guillaume's nickel-steel containing 36 per cent. Ni — have 

 expansion coefficients comparable with that of silica, but 

 experience has shown that while invar is eminently useful 

 for working standards, it is quite unsuitable for primary 

 standards, owing to its large thermal hysteresis. Fused 

 silica, on the contrary, has been found to be practically 

 entirely free from this defect ; it enjoys, in the matter of 

 cost, an enormous advantage over platinum-iridium ; 

 furthermore, in view of the fact that primary standards 

 111 always handled by trained and skilled observers, its 

 comparative fragility is of small consequence. Modern 

 methods of manufacturing and working silica have 

 rendered it possible to construct a silica line-standard 

 metre.__The present model, the first of its kind, consists 

 of a sili,-:, tube into which are fused at its ends opt i. . 1 1 1 \ 

 worked plane parallel slabs of silica. These carry the 

 giaduations, and their undersides are platinised. ' The 

 graduations, defining the metre length, are made by cutting 

 through the platinum film with a ruling diamond. The 

 platinum deposit permits the ruling of verv beautiful clean- 

 edged lines. The bar is supported at the Airy points so 

 that tli- -l.il) are horizontal. The lines are viewed from 

 above through the slabs, and are thus seen to advantage. 

 The apparent length of the standard is independ 

 any change of tilt of the cover-slips which are usr ,1 1,, 

 protect the platinum films. The thickness and position of 

 'li end slabs are so arranged that the image of each 



in iIm " neutral plan.- " c 

 is immersed in water. The silica metre was annealed at 

 about 4,io° C, and shrunk a little more than half a 

 micron in the process. It is anticipated that its future 

 secular variation will be negligible so far as practice is 

 concerned.— Ridsdale Ellis : Tie properties of oil 

 emulsions. p nr t i. — Electrical charge. The electrical 

 charge_ on the globules and the contact potential at 

 the oil-water interface were obtained from measure- 

 ments of the migration velocity in an electric 

 The apparatus used by Whitney and Blake and by 

 Burton for determining velocity of migration were found 

 not to bi accurate, sina thi s did not take into con 

 tion the electrical circulation which taki place, and othei 

 NO. 2176, VOL. 87] 



factors, To avoid these errors a microscopic method was 

 employed, and corrections for electrical circulation and 

 other effects were introduced into the method ol calculating 

 migration velocity. For determining contact potential in 

 presence of electrolytes it was found necessarj to modify 

 the apparatus in order to enable the evolution of gas £t 

 the electrodes to be avoided, which would otherwise pre- 

 vent readings being taken. It was found that the magni- 

 tude of the contact potential at the oil-water interface is 

 of the same order of magnitude for oils of various kinds, 

 whether very pure or containing large amounts of impuri- 

 ties. Further, the contact potential at the oil-water inter- 

 face is of the same order of magnitude as that at the 

 glass-water interface and at the interface between the 

 suspended particles of colloidal metals, lycopodium, quartz, 

 and other substances. From these and other considera- 

 tions it would appear that the contact potential in neutral 

 solution depends almost wholly on the dielectric constants 

 of the suspended particle and of the medium in which it 

 is suspended. The contact potential at the oil-water and 

 glass-water interface is a maximum in neutral or slightly 

 alkaline solutions. Thus the addition of caustic soda at 

 first increases the contact potential at the oil-water inter- 

 lace, but when the concentration exceeds o-ooi N the con- 

 tact potential is diminished, rapidly at first, and then 

 slowly. In the glass-water interface the maximum poten- 

 tial appears to be in neutral solution. If hydrochloric 

 ic id is added the contact potential is reduced very rapidly 

 for small concentrations, but only slowly for comparatively 

 high concentrations. — Dr. W. H. Young : A class of para- 

 metric integrals and their application in the theory of 

 Fourier series. In this paper the following theorem, inter 

 alia, is proved : — If f(x) and r;(.v) are two functions the 



(I+/)" 1 power and (1+ ) power of which respectively 



are summable, and if (a„, /•„), (a„, 0„), be their Fourier 

 constants, then the series the general term of which is 

 (a„n n +i$„B„) cos 116 is the Fourier series of a continuous 

 function, a simple expression for which is given. From 

 this theorem follows as a corollary that if the series 



',;.. o„ + 2„ =) («,«„ + «, B„) 



converges it has 



'I 



f(x)g(x)dn for its sum. and more 



generally it always has this expression for sum when the 

 summation is performed in the Cesaro manner. The 

 method employed is shown also to lead to results of 

 analogous nature, previously known. It involves the study 

 of certain parametric integrals, and of a theorem in the 

 theory of sets of points stated and proved in the paper, 

 to the effect that if a set of points of positive content be 

 shifted bodily a sufficiently small distance along the 

 straight line on which it is situated, it necessarily coincides 

 with its original position as to a sub-set of points the 

 content of which may be made as near as we please to the 

 content of the set. — Dr. W. II. Young : A mode of 

 generating Fourier series. — H. R. A. Matlock : Pendu- 

 lum clocks and their errors. The errors to which pen- 

 dulum clocks are liable may be divided into three classeSi, 

 viz. : — (1) those which may affect free pendulums oscilla- 

 ting in vacuo ; (2) errors depending on the action of the 

 air or gas in which the oscillation takes place; (3) errors; 

 due to the escapement and maintaining mechanism. In 

 good clocks unexplained variations of rate are not un-1 

 common, and may be as large as half a second a clay, or 

 even more. At any rate, a clock the rate of which con-l 

 tinues constant within 1/200,000 for a year or more is i 

 exceptional, and anything which succeeds in securing a 

 constancy of rate better than five parts in a million may 

 be considered an improvement. In discussing the various 

 sources of change of rate, all matters (so far as the author 

 knows) which can alter the period by as much as 10-* 

 are taken into account. It appears that most of the 

 anomalous changes of rate are due to variation of friction 

 in the escapement and maintaining mechanism, which acts- 

 chiefly, but not exclusively, by altering the arc of vibra- 

 tion. A graphic method is given for determining in detail 

 the action of escapements on the period. — Prof. Sydney J. 

 Hickson : Ceratopora, the type of a new family of 



