PART II. : HYDRODYNAMICAL THEORY OF TEMPERATURE OSCILLATIONS. 629 



and if the canal is limited by a perpendicular face at either end, and is of length I, we 

 get as the period of standing oscillations, where v denotes the number of nodes, 



t = 



■21 



h + h' 

 o(p - p) 



(3) 



and this is the equation which has hitherto been used for calculating the period of 

 temperature seiches in lakes. 



§ 19. In arriving at these equations, vertical acceleration has been disregarded, and 

 will be disregarded, in what follows. Second order equations for the motion at the 

 surface of separation of two liquids have been considered by Mr H. J. Priestley,* who 

 concludes that the period given by the First Order Equation is too low. 



§ 20. Dr W. Schmidt,! Vienna, through interest in the observations made in the 

 Wolfgangsee by Dr Exner, has separately investigated the oscillations in a basin 

 of rectangular cross and longitudinal section, and arrives at the equations given 

 above in an elegant manner. He has also experimentally verified his results by 

 noting the period of oscillations in a glass tank, the following being the results of 

 these experiments : — 



1. p = 



1-31 



1 =9 - 65 cm. 



1 =5'0 cm. 



p' = 



1-00 



2 0b , =1-00 sec. 



toh S . = "74 sec. 



h - 



6 - 75 cm. 



*calc. = ' 96 se C- 



*caic = '69 sec. 



h' = 



10'75 cm. 







2. p = 



116 



I =9-65 cm. 



1 =5 - cm. 



P = 



1-00 



W = 1'38 sec. 



t obs , = 1-03 sec. 



h = 



8-15 cm. 



<caic. = 1-30 sec. 



^caic. = "5 sec. 



h' = 



8-95 cm. 







3. P = 



1-058 



1 =9 '65 cm. 



1 =5-0 cm. 



P = 



1-00 



t \>s. =2-19 sec. 



*ot>s. =1*63 sec. 



h = 



7-65 cm. 



£ calc . = 2-09 sec. 



* caIc . = 1 51 sec. 



h' = 



9 - 65 cm. 







4. p = 



1026 



1 =9 '65 cm. 



1 =5-0 cm. 



P = 



1-00 



^obs. = 3-28 sec. 



t obs _ =2-46 sec. 



h = 



8-0 cm. 



^caic. = 3-10 sec. 



* calc . = 2-24 sec. 



h' = 



885 cm. 







§ 21. But, as was found in the case of the ordinary seiche, the rectangular approxi- 

 mation to lakes does not give good results, and it is necessary to use some approximation 

 which takes into account variations in breadth and depth. An extension of Professor 

 Chrystal's Hydrodynamical Theory of Seiches enables this to be done ( Trans. Roy. 

 Soc. Edin., xli. (iii.), p. 599, afterwards referred to as H.T.S.). 



§ 22. In what follows it is assumed that at a depth h! in the lake there is an abrupt 

 change in temperature and therefore in density, the density above this discontinuity 



* Proc. Cambridge Phil. Soc, xv. (iv.), p. 297, 1910. 



t Sitzungsb. K. Akad. JViss. JVien, math.-nat. KL, Bd. cxvii., Abt. iia, Jan. 1908. 

 slip in the equation on page 96, by including n under the square root bracket. 



Dr Schmidt has made a slight 



