OF FLUIDS ON THE MOTION OF PENDULUMS. [83] 



The following are the results : 



Cylinder, No. 1. No. 2. No. 3. 



m, by experiment 0.0400 0.0260 0.0136 



»w, by theory 0.0413 0.0291 0.0113 



Difference - 0.0013 - 0.0031 + 0.0023 



The differences between the results of theory and experiment are perhaps as small as could 

 reasonably be expected, when it is considered that, notwithstanding the delicate nature of the 

 experiments, the numerical values of two constants, m and p, had to be deduced from their 

 results. 



68. This memoir of Coulomb's contains also a notice of a set of experiments with disks 

 and cylinders in which the water was replaced by oil. The experiments with disks shewed 

 that with a given disk the arc of oscillation decreased in geometric progression, and that with 

 different disks the moments of the resistances were as the fourth powers of the diameters. The 

 absolute resistances were greater than in the case of water in the ratio of about 17 - 5 to 1. 

 The details of Coulomb's experiments on cylinders oscillating in oil are entirely omitted. It 

 is merely stated that on making the same cylinders as before, or shorter cylinders when the 

 resistance was too great, oscillate in oil, it was found, conformably with the results obtained 

 with planes, that the coherence of oil was to that of water as 17 to 1. The coherence is here 

 supposed to be measured by that part of the resistance which is proportional to the first power 

 of the velocity. On making a rough calculation of the ratio of the resistances to cylinders 

 oscillating in oil and in water, on the supposition that /y/V for oil is to ^/fi for water as 

 17'5 to 1, as would follow from the experiments on disks if the difference of the specific 

 gravities of the two fluids be neglected, I found that the ratio in question ought to have been 

 somewhere about 100 to 1, instend of only 17 to 1. It would seem from this that the theory 

 of the present paper is not applicable to oil ; but fresh experiments would be required before 

 this point can be considered as established, on account of the theoretical doubt respecting the 

 application of the formulae of Section III. Part I., to extremely fine cylinders, especially 

 in cases in which (/ is large, so that VI is very small. It would be interesting to make 

 out whether what I have called internal friction is or is not of the same nature as viscosity. 

 Coulomb and Dubuat apply the term viscosity to that property of water by virtue of which 

 certain effects are produced which have been shewn in this paper to be perfectly explicable on 

 the theory of internal friction ; whereas Poisson, in one of his memoirs, expressly asserts that 

 the terms in the equations of motion which result from what has been called in this paper 

 internal friction belong to perfect fluids, and have nothing to do with viscosity*. Poisson 

 does not give the slightest hint as to the grounds on which he rested his opinion. 



69. I come now to the experiments of Dubuat, which are contained in an excellent work 

 of his entitled Principes <T Hydraulique, of which the second edition was published in 1786. 



• Journal de I'Ecole Poli/technique, Tom. XIII. p. 95. ■> 



35—2 



