error t days ago, and r the rate. By transposing we may also ob tain r, when we know the errors E and E', at two times separated by an interval t. Take the last two observations of the clockerror, which should be recorded in a book kept for the purpose, and compute the error at the time of your observation, and see how it agrees with your measurement. If the day is cloudy, or no instruments are provided for determining the true time, the experiment may be performed as follows. Compute, as above, the rate and error of the clock. Next take the difference in minutes and seconds between the clock and the watch to be compared. To obtain the exact interval, a few seconds before the beginning of the minute by the watch, note the time given by the clock, and begin counting seconds by the ticks of the pendulum. Then fixing your eyes on the watch, mark the number counted when the seconds' hand is at zero. Repeat two or three times, until you get the interval within a single second. Now correcting this by the error of the clock, taking care to give the proper signs, we get the error of the watch. The next thing is to set the watch so that it shall be correct within a second. For this purpose it must be stopped, by opening it and touching the rim of the balance wheel very carefully with a piece of paper, or other similar object. Set the minute hand a few minutes ahead to allow for the following computation. Subtract the clock-error from the time now given by the watch. It will give the time by the clock, at which if the watch is started it will be exactly right. A few seconds before this time hold the watch horizontally, with the fingers around the rim, and at the precise second turn to the right and then back. The impulse starts the balance-wheel, and the watch will now go, differing from the clock by an amount just equal to the error of the latter. 17. MAKING WEIGHTS. Apparatus. A very delicate balance and set of weights, some sheet metal, a pair of scissors, a millimetre scale, and a small piece of brass, A, weighing about 18.4 grammes. The weights are best made of platinum and aluminium foil; but where expense is a consideration, sheet brass may be used for the heavier, and tin foil for the lighter weights. To improve the appearance of the brass and prevent its rusting it may be tinned, or dipped in a silvering solution, or perhaps better still, coated with nickel. Some steel punches for marking the numbers 0, 1, 2 and 5, a mallet and sheet of lead should also be provided. PROPER METHOD OF WEIGHING. A good balance is so delicate an instrument that the utmost care is needed in using it. The student should thoroughly understand its principle, and know how to test both its accuracy and delicacy. See Measurement of Weights, p. 19. The beam should never be left resting on its knife-edges, or they will become dulled. It is therefore commonly made so that it may be lifted off of them by turning a milled head in front of the balance. A second milled head is also added to raise supports under each scale-pan. To weigh any object the following plan must be pursued. To see if the balance is in good order, lower the supports under the scalepans, then those under the beam, by turning the two milled heads. The long pointer attached to the beam should now swing very slowly from side to side, and finally come to rest at the zero. Replace the supports, and open the glass case which protects the balance from currents of air. The object to be weighed, if metallic and perfectly dry, may be placed directly on the scale-pan, otherwise it should be weighed in a watch-glass whose weight is afterwards determined separately. Now place one of the weights in the opposite scale-pan, and remove the supports first from the pans and then from the beam. This must be done very slowly and carefully. Students are liable to let the beam fall with a jerk on the knife-edges, by which the latter are soon dulled and ruined. An accurate weighing is necessarily a slow process and should never be attempted when one is in a hurry. Moreover, by removing the supports quickly the scale-pans are set swinging, and the beam itself vibrating through a large arc, so that it will not come to rest for a long time. It is better while using the larger weights to lower the supports a very small amount only, and notice which way the index moves. As it is below the beam it always moves towards the lighter side. The smaller weights must be touched only with a pair of forceps, as the moisture of the fingers would soon rust them. Those over 100 grms. may be taken up in the hand by the knob, but no other part of them should be touched. Weights should never be laid down except on the scalepans, or in their places in the box. Now try weighing the piece. of brass A. Lay it on one scale-pan, and a 10 gr. weight on the opposite side. The index moves towards the latter when the supports are removed, as described above. Replace the 10 grs. by 20 grs. This is too heavy, and the index moves the other way. Try the 10 grs. and 5 grs. - too light; add 2 grs.- still too light; another 2 grs.- too heavy; replace the latter by 1 gr. – too light. The weight evidently lies between 18 and 19 grammes. Add the .5 gr., or 500 mgr. - too heavy; substitute the 200 mgr.-too light, and so go on, always following the rule of taking the weights in the order of their sizes, and never adding small weights by guess, or much time will be lost. Having determined the weight within .01 gr., the milligrammes are most easily found by a rider. This consists of a small wire whose weight is just 10 mgr. It is placed on different parts of the beam, which is divided like a steelyard into ten equal parts, which represent milligrammes. Thus if the rider is placed at the point marked 6, or at a distance of .6 the length of one arm of the balance, it produces the same effect as if 6 mgrs. were placed in the scale-pan. It is generally arranged so that it can be moved along the beam without opening the glass case, which protects the latter from dust and currents of air. By taking care to lower the supports of the beam slowly, as recommended above, the swing of the index is made very small; it is sufficient to see if it moves an equal distance on each side of the zero, instead of waiting for it to come absolutely to rest. To make sure that no errror is made in counting the weights, their sum should be taken as they lie in the scale-pan, and also from their vacant places in the box. Decimal weights are made in the ratio of 1, 2 and 5, and their multiples by 10, and its powers. To obtain the 4 and the 9 it is necessary to duplicate either the 1 or the 2. The English adopt the former method, the French the latter. Comparing the two mathematically, we find that using the weights 5, 2, 2, 1, we shall, on an average in ten weighings, remove a weight from box to scale-pan 34 times, of which it will be put back 17 times during the weighing, and the remaining 17 times after the weighing is completed. In the English method, with the weights 5, 2, 1, 1, under the same circumstances the weights are again used 34 times, replaced 15 times during the weighing, and 19 after it. There is therefore no difference in rapidity of one plan over the other. The French system has, however, the great advantage that we may at any time test our weights against one another, since 1+2+2 should equal the 5 weight, and sometimes in weighing, if a mistake is suspected a test may be applied by using the additional weight instead of putting back all the small weights, and adding a larger one, as is necessary in the English system. To meet this difficulty a third 1 gramme weight is sometimes added by English makers. Experiment. To make a set of weights for weighing fractions of a gramme. Four are needed of platinum or brass weighing 500, 200, 200 and 100 mgrs., and four of aluminum, or thick tin foil, weighing 50, 20, 20 and 10 mgrs. The latter should be made first, since being the lightest they are the easiest to adjust. Cut a rectangle of the foil about 3 or 4 centimetres on a side, and weigh it within a milligramme. Now determine its area by measuring its four sides and taking the product of its length by its breadth. If the opposite sides are not equal, take their mean. Let A equal the area, and W the weight of the foil. Evidently WA will equal w, the weight per square millimetre, and 50, 20 and 10 divided by w will give the areas of the required weights. Cut pieces somewhat too large and reduce them to the proper size by the Method of Successive Corrections, p. 10. This is accomplished by weighing each and dividing its excess by w. The quotient shows how much should be cut off. As they cannot easily be enlarged if made too small, and the thickness of the foil may not be the same throughout, pieces should be cut off smaller than the computed excess. Small amounts may be taken from the corners, and when completed one of the latter should be turned up to make it easier to pick them up with the forceps. Finally, lay them on the plate of lead, and stamp their weight in milligrammes on them, with the steel punches and mallet. Do the same with the heavier foil, thus making the 500, 200, 200 and 100 mgrs. weight. More care is needed with them, and the last part of the reduction should be effected with a file. Unless great care is taken, two or three will be spoiled by making them too light, before one of the right weight is obtained. 18. DECANTING GASES. Apparatus. A pneumatic trough, which is best made of wood lined with lead, and painted over with paraffine varnish. A graduated glass tube D, Fig. 14, closed at one end, and holding about 100 cm., a tubulated bell-glass B containing about a litre, with stop-cock Cattached, and two or three dry Florence flasks. The mouths of the latter should be ground, so that they may be closed by a plate of ground glass; to remove the moisture they should be heated in a large sand bath, or over steam pipes. A thermometer is also needed. Experiment. Measure the temperature of the air in the flask A by the thermometer, also its moisture, or rather its dew-point. The latter may be assumed to B A C Fig. 14. A D be the same as that of the room, and obtained from the student, using the meteorological instruments. Now close the flask with the plate of glass, and immerse it neck downwards in the pneumatic trough. It may be kept in this position for any length of time, as the water prevents the air from escaping. Next fill the large graduated vessel B with water, by opening its stop-cock C′ and immersing, then close C and raise it. Now decant the gas into it by pouring, just as you would pour water, only that it ascends instead of falling. When all has been transferred read very carefully the volume, as given by the graduation, also the approximate height of the water inside above that outside the jar. Dividing this difference by 13.6 the specific gravity of mercury, and subtracting the quotient from the height of the barometer, gives the pressure to which the enclosed air is subjected. Its temperature may be assumed equal to that of the water, and it may be regarded as saturated with moisture. Next, to transfer it into the graduated tube D, attach a rubber tube to C, and after fill |