allowed to cool, during both of which operations the times of descent of the mercury from one fixed mark to another are carefully noted through the window, the water being stirred constantly. The times of descent are proportional to the viscosities, if a slight correction be made in each case for the variation in the densities of the mercury and the liquid, with change of temperature. To illustrate the nature of this correction let us take the case of glycerine, μ=k(¤—p) T, where T is the time of falling, and σ and p are the densities of mercury and glycerine respectively. If s and are the corresponding coefficients of expansion, The correction is therefore unnecessary between 0° and 30°, and is only 1 in 1200 from 30° to 70°. For ordinary temperatures it may therefore be neglected. With a relative viscosity-curve thus obtained, and with one good absolute determination, we have the means of calculating the absolute viscosity at any temperature along the range. Conversely, we have the means of estimating small masses of mercury by their speed of flow through glycerine or any other known liquid at a known temperature, or of estimating the mean temperature of the liquid. For example, if a column of liquid be heated from above till its state of temperature becomes constant without the aid of convection, we can here determine the temperature-curve along its length, and in fact employ Forbes's method to determine the thermal conductivity of the liquid at various temperatures. In concluding this description of the methods now being employed for the determination of absolute and relative viscosities, it may be well to remark on the advantages and disadvantages of these methods that have already manifested themselves. In the first place we are dealing with steady motions, and are able to investigate the phenomena attending a constant rate of shearing in the liquid much more satisfactorily than if we observe an oscillating motion such as that of Coulomb's disk or Helmholtz's sphere. The existence of sliding-friction can be directly tested, not only between mercury and the more highly viscous liquids, but also between any two liquids that do not dissolve each other. Thus spheres of water may be used with nearly all the fixed oils, and spheres of oil of cloves (density 10475) or of oil of myrrh (density 1.0189) may be used with water. The apparatus is simple and inexpensive; results may be rapidly obtained when a few standard mercury spheres are preserved. They should be kept in a sample of the viscous liquid to be tested. If a sphere breaks, the pieces should be washed in water and reunited on hard pressed blotting-paper. The quality of oils is often tested by their viscosity, and special viscosimeters on the capillary-tube principle of Poiseuille are used for the purpose. A time-reading through a sample of the oil with a standard mercury sphere offers an expeditious way of testing. If the oil is thin and the mercury falls too fast, a calibrated water sphere may be used instead. A sphere of water of 1 millim. radius, coloured with eosin to be clearly visible, travels at the rate of one inch per hour in castor-oil at 8° C.; and here in parenthesis it may be added that we have by far the simplest method of observing the time-integral of temperature for small ranges. The general method cannot be employed for opaque liquids. as we wish to observe the falling sphere; but it is probable that with a little ingenuity this difficulty could be overcome if the opaque liquid presented itself for examination. The small inertia of the falling sphere, advantageous as it is in exhibiting the slightest variations of temperature, is a serious objection if small solid particles are held in suspension in the liquid. As a rule these particles will avoid the small sphere and not touch it; but in the event of contact occurring there is the likelihood of a permanent union between the two and of the particle being dragged down with the sphere, with consequent loss of speed of the latter. Hence clear liquids must be used. The author wishes to acknowledge his obligations to Prof. Henrici for very kindly rendering available the apparatus of his laboratory for the needs of the above experiments. XLIV. The Attachment of Quartz Fibres. MEMBERS of the Physical Society may remember that in 1887 † I described a method of making fine fibres of glass and other materials, but especially of melted quartz, which latter had properties of great value, rendering them more suitable for experimental work of combined delicacy and accuracy than those of other known materials. Experiments made since by others as well as myself have further shown that for delicate work of the highest degree of accuracy they are essential. The method of fastening them, however, at their ends to the pointed end of the torsion-pin at the top or of the suspension below by shellac varnish, or better by melted shellac, is apt to give rise, more especially if the fibre is unskilfully laid in place so that it is twisted round the point, to a slow creeping of the point of rest due to slow changes in the shellac. This, except for the first few days, can hardly ever be of an amount to seriously affect any observations; in fact I have made many observations of the effect of gravitation between small masses with fibres so fastened of a great degree of accuracy, besides those with the radiomicrometer, pocket electrometer, &c., without any inconvenience, yet I have felt that some method of attaching them which would be less likely to hold the fibre by a part in a state of torsional strain or of flexure would be preferable. If the part of the fibre held could certainly be in its natural position and state with respect to the rest, then, even if the fastening should fail to be as perfect as a true weld, any resulting change of zero should be small compared to that observed where the portion held is twisted or much bent. The process of silvering, electro-coppering, and soldering is an obvious one, but it is not so easily carried out with a fair degree of certainty and in a manner which is convenient of application, as might be expected. My experience of last autumn has enabled me to perform the process in a series of operations, each simple enough, and, as far as I am able to test it in the apparatus with which I am now measuring the Newtonian constant of gravitation (which I may say is of unusual delicacy), with perfect success. In this case the fibre is necessarily stretched to not far from its breaking weight, * Communicated by the Physical Society: read February 23, 1894. † Phil. Mag. June 1887. and it is in such cases that the stability of the fastening is most severely tried. The first thing I found was that it was a mistake to solder the fibre to the torsion-rod and to the suspension directly. The difficulty of the manipulation is great and a change of fibre is very troublesome. The preferable plan is to solder the ends of the fibre to little tags of metal so small and light that they may be picked up by the fibre from anything on which they rest without risk of snapping the fibre at the point of junction. These tags, which are conveniently made of copper-foil, five millimetres long and one millimetre wide about at the wide end, tapering nearly to a point, can afterwards be fastened to the torsion support and the suspension by shellac varnish or by melted shellac, and now the enormous surface and the stiffness of the foil is sufficient to prevent any trouble from the causes to which reference has already been made. These tags might also for some purposes, either or both of them, be made of T-form to hang in a pair of V's, and so dispense with cement altogether, and allow of the easy interchange of suspensions or of fibres, but I have not myself employed such a form. The following operations are those which I have found to answer : 1. Select a fibre of the right diameter to give the desired torsion. Since the torsion depends on the fourth power of the diameter, a small change in the diameter makes a fourfold change in the torsion, and great accuracy of measurement is needed where an exact torsional rigidity is required. Cut off a piece from two to three centimetres longer than will ultimately be required. 2. Fasten to the extreme ends of the fibre, with melted shellac, little weights of gold or platinum heavy enough to pierce a liquid surface. 3. Hang the fibre over a fixed round horizontal rod of wood, 1 centimetre in diameter or thereabouts, so that the little weights hang side by side, and lift up from below a little glass of strong nitric acid, so as to wet and clean the fibre well above the final points of attachment. The vessel must be wide enough to prevent capillarity from drawing the fibres to one side, or it must be brimful so that the surface is convex, which with nitric acid is objectionable. vessel must be moved both upwards and downwards past the place at which the weights pass through the surface very rapidly, practically with a jerk; otherwise the weights will be drawn together by capillarity, and the fibres will get twisted, The or capillarity will give trouble somehow. With the rapid movement the little weights hardly acquire any pendular motion. 4. After a minute or two do the same, but to a slightly greater depth, with water which may be distilled. 5. When the acid may be supposed to be washed off, immerse in the same way in Rochelle salt silvering-solution (Kohlrausch, Physical Measurements,' p. 115). 6 6. Wash as in 4. 7. Fill a glass with the copper solution that is employed in electrolytic measurements of current, i. e. not saturated, and slightly acid. Dip the extreme point of the positive wire from a single cell into the liquid, and with a clean smooth negative wire take the hanging ends, one at a time, and having made the contact outside the glass by resting the upper part of the silver coat upon the wire, let down into the solution, keeping the fibre in gentle movement on the wire and making it dip more and less in the liquid. In a few seconds the little weight will be bright red, and the immersed portion of the silvered coat will be bright red also. The silver coat has sufficient resistance to prevent unduly rapid deposition. Do the same to the other end. 8. Cut off to length, allowing about 5 millimetres at each end for the junction. Take tags of copper-foil three or four centimetres long and three or four millimetres wide, tapering to a point, and having tinned the pointed end of each with the minimum of solder, again wet with chloride-of-zinc solution. On the wet surface lay the coppered end, taking care that it points in the right direction. Capillarity will now hold it. Rapidly heat the copper to the melting-point by holding a point about one centimetre from the narrow end over a minute flame. The solder will flash and envelope the coppered fibre. Cut off the tag of the desired length, holding the metal by the tag with a pair of pliers and not by the heavy end. 9. Wash in boiling water as in 4 to remove chloride of zinc. The fibre is now attached, but the protruding silver and copper give a want of definiteness in the place of attachment. 10. Dip up to the point of the tag in melted beeswax, following the precautions given in 3, but the two tags may be more conveniently dipped separately. 11. Dip up to the top of the copper and silver in strong nitric acid. 12. Wash in boiling water, which removes acid and beeswax and leaves the fibre ready for use. |