OE INTERNAL FRICTION OF AIR AND OTHER GASES. 253 



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 wea-e 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 loga- 

 rithms 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 eridence 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 

 P2 inch per second. The changes of form in the air between the disks were therefore 

 effected very slowly, and eddies were not produced f. 



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 longitudinal strain. The wire used in these expe- 

 riments had been hanging up for some months before, and had been set into torsional 

 vibrations with various weights attached to it, to determine its moment of torsion. Its 

 moment of torsion and its viscosity seem to have remained afterwards nearly constant, 

 till steam was employed to heat the lower part of the apparatus. Its viscosity then 

 increased, and its moment of torsion diminished permanently, but when the apparatus 

 was again heated, no further change seems to have taken place. During each course of 

 experiments, care was taken not to set the disks vibrating beyond the limits of the scale, 

 so that the viscosity of the wire may be supposed constant in each set of experiments. 



* 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. 



