27 6 kepoet — 1879. 



where k is a coefficient depending on torsion, and / is a coefficient depending on 

 friction. 



It is easy to see that the complete integral of the equation of motion 



d 2 x x dx , 72 



dt 2 J dt (3) 



must he of the form 



mi mt 



x — ae cos nt + be sin nt (4) 



where a and b are arbitrary constants, and where m and n have the values 



- - -i 



V *" " T (5) 



If we reckon the time from the commencement of the oscillation, equation (4) 

 reduces to 



mt 



x = ae cos nt (6) 



If T denote the time of a complete double oscillation, we find from the above 



fnT 



e n = e e~' * (7) 



where 8„ = amplitude of the (n + l) th vibration. 

 8 = amplitude of the first vibration. 



From (7) we obtain the following working equation for use in the calculations 

 todetermine the coefficient of friction . 



/-It 10 * (JO (8) 



Also we have 



from which we obtain, after some reductions 



T = ** 



^4k 2 - f 2 ( 9 ) 



If we introduce into this equation the value of / determined by (8) we obtain 

 k, which depends on the torsion only. 



The mean value of/, the coefficient of friction, in air and water, for amplitudes 

 6 ranging up to 360°, was found to be 



/ = 60527 (air) 



/ = sow (water) 



The details of my experiments will be published by the Royal Irish Academy, 

 and will show that the results are very close to each other, and that the method of 

 observation admits of great precision. 



My intention, in commencing the experiments was to ascertain the coefficient 

 of tidal friction, and also to ascertain the elevation of water at the equator or pole, 

 necessary to cause a current ; both these results I hope to secure with some 

 approach to accuracy. 



