and outflow of the water; d is an opening to receive a thermometer. The mode of using the whole apparatus is given in describing Wild's polariscope (§ 49, Fig. 29).

Another arrangement is that adopted in Mitscherlich's large instrument, shown in § 48, Fig. 26, in which the observation-tube is enclosed in a rectangular metal box filled with water.

Or, lastly, the method shown in Fig. 45 may be adopted, in which the tube is laid round with a fine

Fig. 45.

lead spiral through which the water is allowed to flow; the tube itself being provided with two side openings through which the liquid is filled and emptied, and which serve also to hold the thermometers. The two terminal plates can in this case be fixed permanently in their places, for which purpose a solution of isin glass in acetic acid may be used. To prevent loss of heat the lead tubing should be protected by wrapping round it a good layer of flannel.

§ 66. Measurement of Length of Tube.--In the formula for the determination of specific rotation, the length of tube appears as an absolute quantity, so that to render results obtained by different observers comparable, it is necessary to have a uniform standard of measurement; and for this purpose, the first consideration is that the millimetre division on the measure be rigidly accurate.

The determination of the tube-length is frequently left to the instrument-maker. As a means of verifying the ordinary 1 and 2 decimetre tubes, Scheibler1 recommends round brass rods, made accurately 100 and 200 millimetres respectively in length, with flat ends. Screwing a glass plate on one end of the tube, the rod is pushed inside the open end, taking care that it stands straight, and the other glass plate put on, when, if the tube is of the proper length, it should fit exactly, and no room be left for the rod to move about when the whole is shaken.

In all exact experiments, it is necessary to know the length of tube to within at least 0.1 millimetre, and it is therefore desirable to be able oneself to measure it with this degree of precision. Fig. 46 represents an instrument constructed by Feldhausen, mechanician, Aachen, for this purpose, which can be used for ordinary tubes of any

1 Scheibler: Zeitschr. des Vereins für Rübenzuckerindustrie, 1867, 226; 1874, 786.

diameter, as well as for those provided with water-bath surroundings. On two supports AA (A' in the side elevation) is fixed, horizontally, the brass bar BB, 3 decimetres in length, carrying the plate Cfixed at one extremity, and the sliding-piece D. The latter consists of the piece a, which can be firmly clamped by the screw c, and is connected by means of the micrometer-screw d and the spring e with the second piece b, so as to communicate to the latter a fine movement. The bar BB is graduated to millimetres, and the sliding-piece b carries a vernier, reading to th millimetre. Into the face of the fixed plate C Fig. 46. k

and the opposite face of the sliding-piece b, are screwed horizontally two round steel pins mn, to serve as supports for the tube we wish to measure E (which in the Fig. is shown as jacketed). Above the pin m is a wedge of steel f, fixed with its sharp edge vertical, against which one end of the tube is made to rest. A similar steel wedge g, is affixed to the short arm of the bent lever h i, which works on the pivot h; these parts (indicated in the side-view by g'hik) being in connection with the sliding-piece b. The outside of the longer arm, i, which is directed downwards, has a spring p resting upon it, which tends to make it move towards the left; and at its extremity an index mark q is placed which can be made to coincide with a similar mark on b.

In using the instrument the pins m n are first removed by unscrewing, and the sliding-piece D pushed close up to C, until the two edges of the prisms ƒ and g nearly meet. The part a is then clamped, and with the aid of the micrometer-screw d the part b is moved forward, until by perfect contact of the edges f and g, the index mark 4, which at first stood to the left, is made to coincide with the mark on b. This gives the zero-point. The pins m n are then screwed

into their place, D being pushed back far enough to allow of the tube to be measured, being suspended freely upon the pins. One end of the tube is pressed against the edge f, while the contact of g with the opposite end is completed with the micrometer-screw, until the marks at q again coincide. The length is then read off with the vernier on the graduated bar. Since the annular end-surfaces of the tube are never truly parallel, the latter should be turned on its axis through a quarter, half, and three-quarters of a circle, and the mean of the measurements in the several positions taken as the true length. Where a cathetometer is available, the following mode of deter

mining tube-lengths may also be adopted. A piece of glass tubing a b (Fig. 47), of such diameter that it will slide easily inside the tube to be measured without shaking about in it, is closed at one end b with the blowpipe, the glass being drawn to a blunt point, which can then be sharpened off a little with the file. Enough is cut off the open end to leave the tube some millimetres shorter than the tube to be measured, after which it is filled with mercury to about onefourth of its length, the metal being retained in its place by a cork c pressed down on its surface. Into the mouth of the tube is inserted a close-fitting, wellgreased piece of indiarubber tube d, through

which passes a glass rod e, of diameter just sufficient to move easily within the india-rubber collar. To allow escape of air the indiarubber should be slit down its whole length at one side. The ends of the glass rod are drawn out a little, that at f being brought to

a point. The other end is passed through the cork g, so as to ensure straight motion within the tube, and the rod is pushed down so far that the total length of the combination is somewhat greater than that of the tube to be measured. The latter is then closed at one end with glass plate and screw-cap, the contrivance just described slipped into it, and the glass rod pushed down by pressing the point ƒ with the other glass end, and screwing the latter firmly down. The lower screw-cap is now removed, the inner tube withdrawn without disturbing the position of the rod, and fixed in gimbals (Fig. 48), whereby the weight of the mercury in the bottom keeps it truly perpendicular. By means of a cathetometer the distance between ƒ and b can then be determined. Repeated measurements taken in this way are found to agree with a mean variation of only ± 0·02 millimetre. Where the apparatus is too wide and requires steadying in the tube, india-rubber bands, h h (Fig. 47), can be slipped over it.

In determining the angle of rotation of a liquid at different temperatures, the consequent variations in the length of tube must be taken into account. For this purpose it will be found sufficient to take the mean value 0·0000085 as the coefficient ẞ of linear expansion of glass for 1° Cent. Representing the length of tube in millimetres by L and the temperature of measurement by t, the length at any other temperature ť will be given by the formula

Lt [1 + ẞ (t − t)], when t' > t,

Thus if a tube measures exactly 200 millimetres, at a temperature of 20°, it will measure 200.02 millimetres at 30° and 199.98 millimetres at 10°. The correction is therefore only needed for great variations of temperature and long tubes.

C. Estimation of Percentage Composition of Solutions.

§ 67. Preparation of Solutions by Weighing the Active and Inactive Constituents. For this purpose small blown glass flasks (Fig. 49) of 25 to 100 cubic centimetres capacity, with wide necks, and provided with ground-glass stoppers, will be found most suitable. The active substance is first weighed into a flask of this kind, after which the calculated amount of solvent necessary to give the desired percentage is introduced by means, first, of a wide, and subse

quently a narrow-necked pipette. But as in this way a drop or two may be easily added too much, and thus the right percentage not accurately attained, it is best to prepare the solutions roughly at first by weighing in a pair of scales, and afterwards determine accurately by a chemical balance the real amount added.1

Fig. 49.

§ 68. The percentage composition of fresh-prepared solutions can easily be found to the third place of decimals by weighing to milligrammes, but this accuracy vanishes when it becomes necessary to filter from turbidity, the evaporation of the solvent which takes. place during the process, increasing the percentage of non-volatile active substance.

To estimate the magnitude of the error arising from this source, a few experiments were made partly by placing the filtering apparatus bodily into the balance-pan, and partly by determining the percentage after as well as before filtration. Filters of Swedish paper were invariably used, and both the funnels and the other vessels employed were covered over as much as possible.

Aqueous Solutions.-a. 43.131 grammes of water took four minutes to filter, losing 0.019 gramme by evaporation. Temperature of the air 18° Cent. 99.614 grammes of water took eleven minutes to filter, and lost 0.041 gramme by evaporation. Temperature, 20° Cent. At this rate, filtration of 40 to 100 grammes of a 10 per cent. solution would be tantamount to an addition of about 0.004

per cent.

1 Instead of putting the object to be weighed in the left and the weights in the right scale, in the usual way, the following method is convenient :-A certain weight, greater than any likely to be used in the experiments, is put in the left scale. A 50 gramme weight will generally do. In the right scale is placed first the empty flask, together with weights enough to produce equilibrium, and the same process repeated after the substances have been introduced. The advantage of this method is that, as the weight in the balance remains constant, the oscillations remain the same, and, by finding once for all the amount of swing corresponding to 1 milligramme, it will be easy always, when the balance is approaching equilibrium, to fix upon the proper division for the rider from observation of a single oscillation. Thus the process of weighing is facilitated. It is, however, an indispensable condition that the length of beam-arms suffer no alteration during any series of connected weighings. The substitution method (Borda's) of weighing is the only method which meets this difficulty.