abundance of ice and salt to make freezing mixtures; and with no other apparatus than can be made by a moderately skilled glassblower; and with no other standard of physical measurement of any kind than an accurate linear measure. He may assume the force of gravity to be that calculated for his latitude with the ordinary rough allowance for his elevation above the sea, and his omission to measure with higher accuracy the actual force of gravity in his locality can lead him into no thermometric error which is not incomparably less than the inevitable errors in the reproduction and use of the air thermometer, or of mercury or other liquid thermometers. In temperatures above the highest for which mercurysteam pressure is not too great to be practically available, nothing hitherto invented but Deville's air thermometer with hard porcelain bulb suited to resist the high temperature is available for accurate thermometry. The following statement is in the Encyclopædia Britannica article "Heat," appended to the description of steam-pressure thermometers which it contains:-"We have given the steam thermometer as our first example of thermodynamic thermometry because intelligence in thermodynamics has been hitherto much retarded, and the student unnecessarily perplexed, and a mere quicksand has been given as a foundation for thermometry, by building from the beginning on an ideal substance called perfect gas, with none of its properties realised rigorously by any real substance, and with some of them unknown, and utterly unassignable, even by guess. But after having been moved by this reason to give the steam-pressure thermometer as our first theoretical example, we have been led into the preceding carefully detailed examination of its practical qualities, and we have thus become convinced that though hitherto used in scientific investigations only for fixing the "boiling-point," and (through an inevitable natural selection) by practical engineers for knowing the temperatures of their boilers by the pressures indicated by the Bourdon's gauge, it is destined to be of great service both in the strictest scientific thermometry, and as a practical thermometer for a great variety of useful applications." 2. On a Sulphurous Acid Cryophorus. (Abstract.) The instrument exhibited to the Royal Society consisted of a U-shaped glass tube stopped at both ends, containing sulphurous acid liquid and steam. The process by which the sulphurous acid is freed from air, which was partially exhibited to the Royal Society, is as follows: Begin with a glass U tube open at both ends, and attach to each a small convenient, very fine, and perfectly gas-tight, stop-cock. Placing it with the bend down in a freezing mixture, condense pure well-dried sulphurous acid gas direct into it from the generator till it is full nearly to the tops of the two branches. Then close the stop-cock, detach from the generator, and remove from the freezing mixture. Holding it still with the bend down, apply gentle heat to the bend, by a warm hand or by aid of a spirit-lamp, so as to produce boiling, the bubbles rising up in either one or the other of the two branches. After doing this for some time let the bend cool, and apply gentle heat to the surface of the liquid in that one of the branches into which the bubbles passed. With great care now open very slightly the stop-cock at the top of this branch, until the liquid is up to very near the top of the tube, and close the stop-cock before it begins to blow out. Repeat the process several times, causing the bubbles sometimes to rise up one branch, and sometimes up the other. After this has been done two or three dozen times, it is quite certain that only a very infinitesimal amount of air can have remained in the apparatus. When satisfied that this is the case, sink the bend once more into a freezing mixture, and with a convenient blow-pipe and flame melt the glass tube below each stop-cock so as to hermetically seal the two ends of the U tube, and detach them from the stop-cocks. This completes the construction of the sulphurous acid cryophorus. The instrument, if turned with the bend up and the two sealed ends down, may be used as a cryophorus presenting interesting peculiarities. The most interesting qualities are those which it presents when held with the bend down. In this position it constitutes a differential thermometer of exceedingly high sensibility, founded on the difference of sulphurous acid steam-pressure due to difference of pressure in the two branches. One very remarkable and interesting feature is the exceeding sluggishness with which the liquid finds its level in the two branches when the external temperature is absolutely uniform all round. In this respect it presents a most remarkable contrast with a U tube, in other respects similar, but occupied by water and water-steam instead of sulphurous acid and sulphurous-acid-steam. If the U tube of water be suddenly inclined 10 or 20 degrees to the vertical in the plane of the two branches, the water oscillates before it settles with the free surfaces in the two branches at the same level. When the same is done to the U tube of sulphurous acid, it seems to take no notice of gravity; but in the course of several minutes it is seen that the liquid is sinking slowly in one branch and rising in the other towards identity of level. The reason is obvious. 3. Vibrations of a Columnar Vortex. By Sir William Thomson. This is a case of fluid motion, in which the stream lines are approximately circles, with their centres in one line (the axis of the vortex) and the velocities approximately constant, and approximately equal at equal distances from the axis. As a preliminary to treating it, it is convenient to express the equations of motion of a homogeneous incompressible inviscid fluid (the description of fluid to which the present investigation is confined) in terms of "columnar co-ordinates" r, 0, z, that is co-ordinates such that r cos = x, r sin 0=y. If we call the density unity, and if we denote by x, y, ż the velocity-components of the fluid particle which at time t is passing d d d d through the point (x, y, z); and by dt' dx' dy' dz differentiations respectively on the supposition of x, y, z constant, t, y, z constant, t, x, z constant, and t, x, y constant, the ordinary equations of motion are VOL. X. 3 н To transform to the columnar co-ordinates we have (2). = + dx 0 Now let the motion be approximately in circles round Oz, with velocity everywhere approximately equal to T, a function of r; and to fulfil these conditions assume where g, r, w, and are functions of r, each infinitely small, in comparison with T. Substituting in (4) and (5) and neglecting squares and products of the infinitely small quantities we find, Taking (7), eliminating, and resolving for g, r, we find For the particular case of m=0, or motion in two dimensions (r, 0), it is convenient to put In this case the motion which superimposed on r = 0 and rẻ = T gives the disturbed motion is irrotational, and sin (nt – ¿0) is its velocity-potential. It is also to be remarked that when m does not vanish the superimposed motion is irrotational where if at all, and only where, T const./r, and that whenever it is irrotational given by (10) is its velocity potential. = as Eliminating g and from (8) by (9) we have a linear differential equation of the second order for w. The integration of this, and substitutions of the result in (9), give w, g, and r, in terms of r and the two arbitrary constants of integration which, with m, n, and i, are to be determined to fulfil whatever surface conditions, or initial conditions, or conditions of maintenance, are prescribed for any particular problem. |