OF FLUIDS ON THF. MOTION OF PENDULUMS. [65] 



2a 2 (6 3 — a 8 ) -1 or 2a*b~* nearly, which is obtained from the ordinary equations of hydrody- 

 namics, and therefore it cannot be regarded as more than a rude approximation. It will be 

 useful, however, as affording an estimate of the magnitude of the effect produced by confining 

 the air. The diameter of the vacuum tube (whether external or internal is not specified) is 

 stated to have been six inches and a half, whence 2 b = 6-5. The values of k given in the next 

 column are obtained by applying the correction for confined space to Baily's values of n, and 

 subtracting unity. The value of HI corresponding to each value of k was got by interpolation 

 from the table near the end of Section III. of the former part of this paper. For k = 1-Q23 

 the interpolation is easy. The value 3081 happens to be almost exactly found in the table. 

 For k = 6*530, a remark already made will be found to be of importance, namely, that the 

 first differences of ttt 2 (& — l) are nearly constant. The last column contains the value of ^//u' 

 obtained from the equation 



a / 7r 



m = 2 -V M v 0^7) 



which contains the definition of tit. 



It will be observed that the three values of -y/V' are nearly identical. Of course any 

 theory professing to account for a set of experiments by means of a particular value of a dis- 

 posable constant, when applied to the experiments would lead to nearly the same numerical 

 value of the constant if the experiments were made under nearly the same circumstances. 

 But in the present case the circumstances of the experiments are widely different. The dia- 

 meter of the steel rod is little more than the sixth part of that of the copper rod, and the 

 value of k obtained by experiment for the steel rod is more than three times as great as that 

 obtained for the copper rod. It is a simple consequence of the ordinary theory of hydro- 

 dynamics that in the case of a long rod oscillating in an unlimited fluid k = I, and we see that 

 this value of k must be multiplied, in round numbers, by 2, by 3, and by 6^, in order to 

 account for the observed effect. The value 1-5445 of ttt is so large that the descending series 

 comes into play in the calculation of the function k, while 0-2822 is so small that the ascend- 

 ing series are rapidly convergent. Hence the near agreement of the values of -y/V deduced 

 from the three experiments is a striking confirmation of the theory. The mean of the three is 

 01 158, but of course the last figure cannot be trusted. I shall accordingly assume as the 

 value of the square root of the index of friction of air in its average state of pressure, tempe- 

 rature, and moisture 



VV = 0'116. 



It is to be remembered that .y/V expresses a length divided by the square root of a time, 

 and that the numerical value above given is adapted to an English inch as the unit of length, 

 and a second of mean solar time as the unit of time. 



56. I now proceed to compare the observed values of tl with those calculated from 

 theory with the assumed value of -y//a. I begin with the same cylindrical rods as before, 

 together with the long brass tubes Nos. 35 to 38. The diameter of this tube was 1-5 inch, 

 and its length 56 inches. The ends were open, but as the included air was treated by Mr 

 Baily in the reduction of his experiments as if it formed part of the pendulum, we may regard 

 Vol. IX. Part II. 33 



