mass, and m and r have the same meanings as The actual centrifugal apparatus describe developed by the Central Scientific Company. fects of earlier forms have been avoided in th tion is reduced to a minimum and the increa force with increased values of r is balanced by increase in the centripetal force exerted by a s ing greater stability. A rectangular frame of F H Fig. 7. ted with a spindle at the mid-point of one long ment to the rotator. Two equal, cylindrical n are so mounted as to counterbalance each othe position, but A is supported on pivots at P, S frame is revolved A will exert a centrifugal for to swing outward, thus raising the pointer, F. tension of which is adjustable by the knurled so the centripetal force by which the tendency of ward is restrained. Lines are etched at C on th and at AP in the plane of the center of mass radius of rotation, r, can readily be measure cylinder, A, will be given by the instructor. This mass is called M. It is necessary to have a motor-driven rotator, with accurate speed control and revolution counter, for hand-driven apparatus cannot be run at a sufficiently uniform rate. A stop-watch or ordinary watch with second-hand will also be needed. Clamp the apparatus in the rotator chuck, set the motor going and adjust the speed until the pointer, F, is just opposite the edge of the indicator, D. When this condition is obtained, the number of revolutions made in some definite time must be determined by the use of the revolution counter and watch, and n, the number of revolutions per second, computed. During this time, the pointer, F, must be kept at the edge of D, by changes in speed if necessary. Several runs should be made and the average value of n thus found should be used in the equation. These runs should agree very closely among themselves. Measurer with the vernier calipers, while A is held so that the pointer is opposite the edge of D. All the data for use in equation (2) are now known and the value of ƒ can be computed. It is necessary to make a correction for the centrifugal effect on the spring. Find m, the mass of the spring, and l, its length when extended as it was while the mass was revolving. It has been found by analysis too difficult for this book, that the proper correction. to apply for a spring symmetrically placed with respect to the axis of rotation is given by the equation, 2 C - π2 n2 m l. 3 (3) Add this correction to the force obtained from equation (2). These values will be in dynes. Now to check this value, remove the frame from the rotator and suspend it from a support with B uppermost. Pass a fine wire through the loop, E, on cylinder A, and suspend on the wire weights sufficient to bring the pointer, F, opposite the edge of D, as it was during the rotation. This weight plus the weight of A, all expressed in dynes, should agree with the force found from the first part of the experiment within a very few per cent. Several trials can be made with tensions varying somewhat each time. HEAT EXPERIMENT NO. 201 THE MERCURY THERMOMETER. References: Stewart, Physics, Sect. 184, 185; Kimball, College Physics, Sect..366, 370; Duff, College Physics, Sect. 177, 178; Spinney, Text-Book of Physics, Sect. 156-158. As no mercury thermometer gives correct readings throughout its entire range, it is necessary to calibrate all thermometers used where temperatures must be accurately determined. The purpose of this experiment is to show how such a calibration may be carried out. (a) On the Centigrade scale, zero degrees is defined as the temperature of melting ice, and one hundred degrees as the temperature of the steam over pure water boiling under standard atmospheric pressure. These two temperatures are used as the fixed points of the thermometer scale. This part of the experiment is a test of the fixed points of the thermometer. Make a mixture of finely crushed ice and water, so that there is ice throughout the mixture and not merely at the top. Immerse the thermometer bulb in the mixture so that the entire mercury column is below the surface. Wait several minutes until you are sure the mercury has ceased falling, and then obtain the reading. Estimate tenths of degrees, using a small magnifier if necessary. Fill the boiler about half full of water and place the thermometer in the upright tube so that the 100° mark is just visible. Boil the water vigorously for several minutes until the mercury has ceased to rise in the thermometer tube, and observe the reading carefully. Obtain the barometric reading (note that the barometer reading in centimeters must be used). Taking the boiling point of water as 100° when the barometer reads 76 centimeters, find the boiling temperature under the observed barometic pressure. To do this, remember that near 100°C an increase of approximately 27 mm. in the barometric height raises the boiling point by one whole degree Centigrade, and an equal decrease lowers the boiling point the same amount. Check your result by referring to a table of boiling points of water. Now allow the thermometer to cool to the temperature of the room and again determine the reading for the freezing point. Compute and record the corrections to be applied to the readings of the thermometer under observation at the boiling and freezing points. Find the differences between the observed temperature readings and the correct ones. A correction is positive, if it is to be added to the reading of the thermometer in order to give the correct temperature, and negative, if it is to be subtracted. Record the number of the thermometer tested. A rough calibration curve may be made by plotting the degrees marked on the thermometer scale as abscissæ and the corrections as ordinates, locating the corrections at the freezing and boiling points, and then connecting the two points by a straight line. This obviously takes no account of irregularities in the diameter of the tube. (b) To determine the errors of the thermometer for intermediate points, a standard thermometer is used for comparison. Place your thermometer and the standard in a vessel of water and raise the temperature of the water to about 10°C. Read both thermometers accurately, to one-tenth of a degree. Then raise the temperature to 20°, 30°, etc., up to 90°, each time removing the flame and stirring before reading. Arrange the data in tabular form. In one column is to be recorded the "True Temperature," obtained by correcting the reading cf the standard by means of the curve given out with the instrument. From the curve the true temperatures are computed by adding to the readings of the standard the corresponding corrections shown on the curve. Knowing the true temperatures corresponding to any readings of the thermometer under examination, a column headed "Corrections to Thermometer Reading" may be formed. Use these corrections as ordinates and readings of your thermometer as abscissæ and plot a curve for your thermometer similar to the one for the standard. Record the numbers on the thermometers used. EXPERIMENT NO. 202 LINEAR EXPANSION. References: Stewart, Physics, Seet. 195; Kimball, College Physics, Sect. 379, 381; Duff, College Physics, Sect. 181; Spinney, Text-book of Physics, Sect. 160. In order to calculate how much expansion a certain temperature change will cause in a given metal object, it is necessary to know the coefficient of linear expansion of the metal. This coefficient is defined as the change of length of unit length of the substance under a temperature change of one degree. The determination of the coefficient involves, therefore, the measurement of the length of a rod of the material, and of the change in length for a known change in temperature. Rods 60 to 70 cm long are commonly used. Some instrument capable of accurately measuring very small distances must be employed for finding the amount of expansion. Two methods will be described. (a) The rod, surrounded by a metal jacket through which steam can be passed, is set vertically in a suitable frame with the rear leg of an optical lever on top of the rod. The other legs of the lever rest on the frame. A thermometer is set in a side tube of the jacket. Readings of the lever are taken with telescope and scale. First read the thermometer and the scale when the bar is at room temperature, then pass steam through the jacket for several minutes until the thermometer ceases to rise. Read the scale again and compute the actual elongation of the rod by the method described in Experiment No. 118. Owing to the fact that a long mercury column in, the thermometer is not exposed to the steam, the thermometer usually will indicate a temperature somewhat lower than the correct boiling point. To find the real temperature of the rod when hot, it will be better to read the barometer and compute the boiling point as described in Experiment No. 201. (b) In the micrometer type of apparatus, the bar in its jacket is mounted horizontally in a frame. The rod rests against a set-screw at one end and a micrometer screw may be brought into contact with the other end. In order to determine accurately when contact is made, the two screws are connected in |