PART IV. : EXPERIMENTAL VERIFICATION OF HYDRODYNAMICAL THEORY. 639 



with the parabolic bottom, and then with the ends rising vertically from the ends of the 

 surface of separation. 



§ 43. The density of the paraffin used was determined by accurate weighing, and at a 

 temperature of 15° C. was found to be "805. A temperature coefficient of '001 per °C. 

 was used to correct for variations in temperature during the course of the observations. 

 The temperature during the observations varied from 12° to 17°. The density of 

 water was taken as '999 throughout, and the value of g as 981. 



§ 44. The following are the observations made in the long trough. T obs is the 

 observed period of the oscillations, T calc the period calculated according to the formula 



T = 



TrlJpR' + p'll 

 \/2g(p-p)H.hi' 



■ (7) 



and T cori . the calculated period after applying a correction for the deviation of the 

 temperature normal curve from the parabolic. The possible error in the results is 

 discussed later. The column headed " plain parabolic " gives the period when the ends 

 of the trough were not truncated, and " truncated parabolic " where they were truncated 

 just above the surface of separation. All measurements are given in C.G.S. units. 



/. 



h. 



h'. 



1140 



7-20 



3-35 



114-0 



720 



440 



114-0 



7-20 



6-10 



106-5 



6-50 



2-00 



106-5 



6-50 



6-50 



T„ 



Plain 

 Parabolic. 



11-12+ 10 



10-27 ±-10 

 9-40 ±07 



8-98 ±-06 



Truncated 

 Parabolic. 



12-6 ±-6 



8-82 ± -09 



T 



' corr. 



Temp. 



11-35 



11-0 



15° 



10-46 



10-2 



15° 



959 



9-4 



15° 



12-8 



12-4 



16° 



9-08 



8-95 



16° 



§ 45. One of the observations gave a period which does not agree with calculation. 

 When £=114, A = 7"20 and h' 3*35, and the basin plain parabolic, repeated observation 

 gave an oscillation with a period of 5 '24 ±"01 sees. Calculation gives as the uninodal 

 period 6"45 sees., and for the trinodal 4'65 sees. The observed period lies between these 

 values. At the time when the observation was made, it was not known what the periods 

 should be, according to the theory, and special attention was not directed to these 

 observations. We have not been able to arrive at any conclusion as to the mode of 

 this particular oscillation. At first it was believed to be the uninodal oscillation ; but 

 subsequent observation showed that the uninodal period was 11*1 sees., and we failed 

 to obtain again an oscillation with a period of 5 '2 sees.* 



§ 46. A more exact series of observations was made in a trough specially designed 

 for the purpose. A parabola was accurately cut out from a block of teak about 10 cm. 

 thick. The equation to the parabola was y = cc 2 /30-48, unit 1 cm., or y = x 2 , unit 1 foot 



* Some serious observational error is suspected. 



