Mat 23, 1913] 



SCIENCE 



805 



retardation r is taken to be proportional to 

 the velocity V for this low velocity, 



at ' 



dV 



-y- = Cdt, 



and 



log V=zCt + K 



will express the value of the velocity at dif- 

 ferent times. In order to determine the 

 constants and K, the ring was held in a 

 vertical position until the colder water near 

 the east wall produced a considerable motion. 

 It was then brought back to the horizontal 

 and the time observed which was required to 

 move successive quarter millimeters. A few 



Fig. 2 



such readings are given in Table II. From a 

 large number of such observations an average 

 curve was drawn, showing the relation of the 

 distance covered to the time (Fig. 2, Curve 

 A). The slope of this curve was taken at two 



Distance in Mm. 



Time in 

 seconds. 



of the most definite points, t ^- 12.5 and 

 t = 30, and these values were substituted in 

 equation (1) to determine the constants C 

 and K. The curve in Fig. 3 was then drawn 

 from the resulting formula, showing the 

 velocity at any time. Curve B, Fig. 2, was 



then constructed by integrating this curve 

 graphically with respect to t. 



The water in the ring has its maximum 

 velocity just before the turn is completed. 

 The time required to make a complete turn 

 was three seconds, and if this is subtracted 

 from the time in column 1, Table I., it gives 

 the length of time between the completion of 

 the turn and the first observation of the 

 motion (column 4, Table I.). Now if a por- 

 tion of Curve B (Fig. 2) be taken, such that 

 the distance represented on the curve in the 

 time of any particular reading is the same as 

 the distance in that reading, the beginning of 

 that portion of the curve will correspond to 

 the time at which the motion of the globules 



was first observed (column 5, Table L). So 

 if the number of seconds in column four is 

 subtracted from the time corresponding to the 

 beginning of the reading, the time correspond- 

 ing to the completion of the turn is obtained, 

 and the velocity at that time can be read from 

 the curve in Fig. 3. This value is given in 

 column six, and is the velocity at the time of 

 completing the turn. The velocities in each 

 of the four cases are averaged separately, and 

 the average of the four averages is taken as 

 the true motion due to the earth's rotation. 



The average of the velocities in these four 

 cases is .0513 mm. per second. From the 

 formula V = ar sin <f> derived above, we ob- 



