6 ox THE vraooemr OR INTERNAL FRICTION 



in these experiments is so accurately geometrical, that no appreciable difference 

 between the results of the two methods would occur. 



The logarithm of each term of the series was then taken, and the mean 

 logarithmic decrement ascertained by taking the difference of the first and last, 

 of the second and last but one, and so on, multiplying each difference by the 

 interval of the terms, and dividing the sum of the products by the sum of 

 the squares of these intervals. Thus, if fifty observations were taken of the 

 extreme limits of vibration, these were first combined by tens, so as to form 

 five terms of a decreasing series. The logarithms of these terms were then 

 taken. Twice the difference of the first and fifth of these logarithms was then 

 added to the difference of the second and third, and the result divided by 

 ten for the mean logarithmic decrement in five complete vibrations. 



The times were then treated in the same way to get the mean time of 

 five vibrations. The numbers representing the logarithmic decrement, and the 

 time for five vibrations, were entered as the result of each experiment*. 



The series found from ten different experiments were examined to discover 

 any departure from uniformity in the logarithmic decrement depending on the 

 amplitude of vibration. The logarithmic decrement was found to be constant 

 in each experiment to within the limits of probable error; the deviations from 

 uniformity were sometimes in one direction and sometimes in the opposite, and 

 the ten experiments when combined gave no evidence of any law of increase 

 or diminution of the logarithmic decrement as the amplitudes decrease. The 

 forces which retard the disks are therefore as the first power of the velocity, 

 and there is no evidence of any force varying with the square of the velocity, 

 such as is produced when bodies move rapidly through the air. In these 

 experiments the maximum velocity of the circumference of the moving disks 

 was about ^ inch per second. The changes of form in the air between the 

 disks were therefore effected very slowly, and eddies were not produced t. 



The retardation of the motion of the disks is, however, not due entirely 

 to the action of the air, since the suspension wire has a viscosity of its own, 

 which must be estimated separately. Professor W. Thomson has observed great 

 changes in the viscosity of wires after being subjected to torsion and longi- 

 tudinal strain. The wire used in these experiments had been hanging up for 



* See Table II. 



t The total moment of the resistances never exceeded that of the weight of ^ grain acting at the edge 

 of the disks. 



