Rate response curves can be calculated according to the following set of equa- 

 tions : 



Let T = indicated temperature recorded by the bathythermograph 

 at any time 9. 



Let To = initial temperature of bathythermograph. 



Let T» = actual temperature of surroundings of bathythermograph. 



Let T =: a constant. 



Then: dTT = -1 /^ _ <y) (i) 



For T.1 = constant, the solution to (1) is as follows: 



^^1^= ,-^ (2) 



m _ m e T 



Tau may be experimentally determined as follows: Assume the BT is moved 

 suddenly from To to Ta (which is experimentally done by plunging the BT suddenly 

 into a cold bath for instance) . 



The relative response conditions at time 9 = x, would be as follows: 



T-T, __ ^-. 



T — T (2a) 



Rearranging : 



T° ll" - 1 -i^ 0-632 (2b) 



Where Ti = indicated temperature at time Q=t: 



Since To - Ta is the total change that the BT would undergo, and To - Ti is the 

 change actually gone through at time 9 = x , one has only to register the time at 

 which the BT records a temperature approximately 63 7^^ of the way between the 

 initial temperature and the bath temperature. Time value is numerically equivalent 

 to X, the response constant of the BT. 



Normally the response time is reported for such instruments, and represents 

 the time to travel 63% of the desired scale limits. 



There have been many questions which have arisen with regard to the response 

 characteristics of the instrument. These questions all point to a definite need for 

 more experimental programs to be undertaken with regard to rate response. Rate 

 response knowledge is important in order to differentiate between this type of hys- 

 teresis and the hysteresis resulting from ocean variabilities. 



5.3.3. Hysteresis Due to Ocean Variability 



The up and down traces may not coincide in portions of the BT trace because 

 of a change in the ocean conditions between the time the downtrace was made and 

 the uptrace was made. This notably occurs in the presence of internal waves. This is 

 not an error of the instrument, but is a true measure of ocean variability. However, 

 as previously pointed out, ocean variability cannot be distinguished from instrument 

 error in any one given set of data except by independent means of checking. 



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