ture depth trace in a horizontal or vertical direction, or both, in order to have the 

 temperature depth trace coincide with the actual values of depth and temperature 

 of the ocean. This necessary translation is called depth set or temperature set. These 

 depth and temperature sets and their corresponding correction factors (known as 

 DCS and TCS) are, according to the terminology described above, determinate 

 errors. These errors are determinate because they have definite magnitude and di- 

 rection of sign and can be duly accounted for. 



4.2. Indeterminate Errors of the Bathythermograph 



The set of the Bathythermograph can change from time to time because of 

 various factors which will be discussed later. This variation in set is then the inde- 

 terminate error contained in the determinate error. 



In addition there are many other indeterminate errors to which the Bathyther- 

 mograph is subject. (1) The Bathythermograph has an inherent reproducibility. 

 (2) It may be subject to a hysteresis error. (3) It may have an error due to the 

 rate of response of the instrument. (4) It may have an error due to operational 

 conditions. (5) It may also have an error imposed upon it when corrections of the 

 slides for the set are made. (6) When the slides are read they are subjected to read- 

 ing errors. (7) Errors in temperatures may result from errors in depth. (8) Errors 

 in initial calibration can produce calibration errors; and finally, (9) the error of 

 the instrument can be a function of the depth, producing a variance in the error. 



4.3. Bathythermograph deviations as a Function of Errors and Ocean Variability 



It may be assumed, therefore, that in a series of temperature measurements in 

 a fixed position in the ocean the average or standard deviation observed will be a 

 function of the ocean variability and the errors involved in the instruments used to 

 make the measurement. The relationship between the standard deviation and its 

 various components again is given by Equation 1 which relates overall error and the 

 contributions which make up the error. 



AE = \/(AEj' + (AEJ' 4- •■• + (AEJ= =\/ E(AE)' (D 



Concerning ourselves with standard deviations which are the correct deviations 

 to employ where random error is involved, Equation 1 is rewritten as follows : 



o 



TOTAL 



^'-''■'OCEAN "^ ^ '■'^•' INSTRUMENT ^ ' 



Where sigma equals standard deviation 



Segregating the standard deviation into the standard deviation of temperature 

 and standard deviation of depth, the following equation can be written : 



^^T/TOTAL V ^(o^JoCEAN "*" ^ '-''t/ INS TRUMEN T ^' 



The standard temperature deviations of the ocean and the instrument can be 

 further broken down into their dependent and independent functions as follows : 



^''t/QCEAN ^ ^^^T/INDEP "*" ^^^T^DEP ^ ' 



^^t)iNST ^^C^TMNDEP "*" ^^'^T^DEP (5) 



