PART IV. : EXPERIMENTAL VERIFICATION OF HYDRODYNAMICAL THEORY. 641 











T 



-'-obs. 



sees. 











No. of 



I. 



h. 



h'. 







T 



- 1 - calc. 



T 



x corr. 



Temp. 



-*-obs./ -'-corr. 







Exp. 



cm. 



cm. 



cm. 



Plain 



Truncated 



sees. 



sees. 



°C 











Parabolic. 



Parabolic. 











1 



5284 



22-90 



7-25 



355 + -05 



3-52 + -01 



3-66 



3-55 



14-5 



•994 



2 



52-84 



22-90 



1-95 





5-78 ±-04 



5-89 



5-70 



16-5 



1-014 



3 



52 84 



22-90 



1-90 



5-83 + -05 





5-97 



5-80 



14-5 



1-005 



4 



43-54 



15-55 



14-65 



2-79 + -02 





2-83 



2-80 



15-0 



•997 



5 



43-48 



15-50 



14-60 



2-78 ±-01 





2-83 



2-80 



15-0 



•993 



6 



43-26 



15-35 



14-85 





267 +01 



2-82 



2-75 



17-0 



•971 



7 



43-26 



15-35 



7-43 



3-05 + -03 



3-05 + -01* 



3- 17 



3-10 



15-0 



•984 



8 



43-26 



15-35 



2-35 



4-48 + -03 



4-46 ± -02 t 



460 



4-50 



15-0 



•993 



9 



43-11 



15-25 



15-10 



2-65 + -01 





2-81 



2-75 



15-5 



•964 



10 



42-98 



15-15 



15-25 



2-73 + -02 



... 



2-81 



2-75 



14-0 



•992 



11 



42-48 



14-80 



15-00 



2-75 ±-03 



• •• 



2-79 



2-75 



15-0 



1-000 



121 



31-22 



8-00 



2-25 





3-44 + -05 



3-61 



3-50 



16-0 



•983 



13 



30-64 



7-70 



22-00 





2-29 ±-02 



2 41 



2-35 



160 



•974 



14 



30-54 



7-65 



22-00 



2-31 + -05 





2-41 



2-35 



14-5 



•983 



15 



30-54 



7-65 



12-50 



2-36 + -01 



2-37 ±-02 



2-47 



2-40 



14-5 



■983 



16 



30-54 



7-65 



6 55 



2-62 + -03 



2-62+02 



2-70 



2-65 



130 



•987 



17 



30-54 



7-65 



2-30 



351 + -05 



3-50 ±-02 



3-55 



3-45 



12-0 



1-016 



18 



21-38 



3-75 



2-70 



2-57+03 





2-67 



2-60 



16-5 



•988 



* A second determination gave T i) S . = 3 "01 + "01. 



t The first observations made gave T bs. = 4'61, but some large error was apparently introduced. 



+ In this case the surface of separation was slightly above the point where the vertical ends began. 



§ 49. Experiments were also made where the cross-section of the trough was as 

 shown in figs. 7 and 8, the ends being truncated. The results of these experiments 

 were as follows : — 



1 



I 

 Shape. 



1 cm. 



h. 

 cm. 



h'. 



cm. 



Breadth of 



Surface of 



Separation. 



cm. 



Breadth of 



Free Surface. 



cm. 



. T 



-■-obs. 



sees. 



T 



- 1 - calc. 



sees. 



2-50 

 2-62 



T 



x corr. 



sees. 



Temp. 



Fig. 7 43-06 

 Fig. 8 43-06 



15-20 

 15-20 



15-05 

 14-90 



5-72 

 5-72 



10-80 

 10-80 



2-41 + -02 

 2-53 ±-01 



2-45 



2-58 



14-5° C. 

 15-5° 



The formula used for calculating the period was as follows : — 



t = 



*\A(/^ 



\'+p 



H 



S- 



•gip-?) 



H.H' 



h.h' 



A . A', b 2 



TrlJbjphH'A' + p'.h'.II.A) 

 J2g(p- P ')B..W.A.A'. 



(8) 



where b is the breadth at the surface of separation, A the maximum area of the 

 cross-section of the lower liquid, and A' the area of the cross-section of the upper 

 liquid. H and H 7 have the meaning assigned in § 40. 



§ 50. An attempt was made to start oscillations when the shape was as in fig. 7, 

 but with the surface of separation a little above the sudden change in breadth. Under 

 these conditions it was found impossible to start a pure oscillation. This case is 

 analogous to that of a lake basin where there is a shelf at the surface of separation. 



§ 51. The greatest difference between the mean observed value for T and the cal- 

 culated and corrected value is 3 "6 per cent. — in most cases it is much less. Examining 

 the case where the difference is greatest (viz. No. 9), assuming an error of '5 mm. in 



