SUBSURFACE TEMPERATURES 



(3) Errors of the breaking-off device . The errors 

 arising from this source can be examined by repeating 

 with the shortest possible interval of time the determi- 

 nation of the zero point of the thermometer or by com- 

 parisons between a perfect and an imperfect thermome- 

 ter. The number of thermometers which do not function 

 properly, according to Bohnecke's experience, is very 

 small and the errors are seldom greater than + 0.'02. 

 The possible errors are probably somewhat greater for 

 the one-temth thermometers and the lim'ts are estimated 

 to be + 0.°03. It happens, however, that the imperfect 

 thermometers behave erratically and give readings 

 which must be rejected because they are obviously 

 wrong. Even a thermometer which as a rule functions 

 reliably may for unl<nown reasons give erroneous re- 

 sults, but such cases ordinarily can be detected, expe- 

 cially if two thermometers have been attached to the 

 same water bottle. 



The preceding discussion can be summarized as fol- 

 lows: 



Source 

 of error 



Thermometer 

 graduated to 1/20' 



Proba- 

 ble 

 error 



Maxi- 

 mum 

 error 



Thermometer 

 graduated to 1/10" 



Proba- 

 ble 

 error 



Maxi - 

 mum 

 error 



(1) Reading 

 (2aj Reduction 

 (2b) Limited ac- 

 curacy of 

 test 

 (2c) Change of 

 zero point 

 (3) Breaking- 

 off device 



±0.003 ±0.005 

 0.000 ±0.002 



±0.005 ±0.01 

 0.000 ±0.002 



±0.003 ±0.005 

 0.02 to 

 0.035 



•0.015 



±0.003 

 -0.02 



±0.n05 

 + 0.02 to 

 -0.08 



0.000 



:0.02 



0.000 ±1.03 



The probable error of a single temperature deter- 

 mination by means of a one-twentieth thermometer not 

 again examined after the PTR test, according to this 

 compilation, lies between the limits -O.'OOO and -0.''021, 

 and the possible errors lie between the limits 0.°052and 

 -0.067. The corresponding limits in the case of a ther- 

 mometer which is graduated to 0.°1 are -0."'012 to -0.''026 

 and 0.'067 to -0.'127, respectively. These limits are only 

 approximate and especially the maximum errors must 

 be regarded as roughly estimated and probably too great, 

 but they furnish a basis for a discussion of the possible 

 differences between the indications of two thermometers 

 used simultaneously. 



The differences between the indications of two ther- 

 mometers which have been used together can be ascribed 

 to the same sources as the errors of one single ther- 

 mometer and we can, therefore, discuss these differen- 

 ces in the same sequence. 



(1) Differences owing to errors of reading. Taking 

 account of the maximum errors as stated in the preced- 

 ing paragraph, these differences may reach +0.°01 and 

 + 0.°02 respectively, but are, as a rule, considerably 

 smaller than +0°01 and disappear when averaging many 

 comparisons. 



(2a) Differences arising from reduction errors . 

 These differences are always negligible because the 

 possible reduction errors, which are smaller than 

 0.°002, have the same sign for both thermometers. 



(2b) Differences owing to errors arising from limit 

 of accuracy of the test . These differences are systematic 



for a given pair of thermometers but cannot exceed 

 + 0.°01. 



(2c) Differences owing to change of zero point . The 

 differences owing to changes of the zero point may reach 

 appreciable values because it is not probable that the 

 zero points of two thermometers change in the same 

 amount although the changes may have the same sign for 

 both thermom'Hers. The difference has a systematic 

 character and is not eliminated when forming the mean 

 value from many comparisons. If two thermometers are 

 compared during a long period, it is to be expected that 

 the difference will change in the course of time because 

 it is not probable that the changes of the zero points of 

 the two thermometers are at the same rate. Further- 

 more it must be expected that a new thermometer will 

 give slightly lower temperatures than an old thermome- 

 ter because the zero point of the older thermometer has 

 risen more. The differences owing to change of zero 

 point, according to the experiences of Dr. Bohnecke, may 

 amount to 0.°055 for the one-twentieth thermometers and 

 to 0.°10 for the one-tenth thermometers. The sign of the 

 difference depends only on whether the indication of the 

 thermometer giving the lowest reading is subtracted 

 from the others or vice versa. 



(3) Differences arising from errors of the breaking - 

 off device. These differences may amount to ±0.°04 or 

 + 0.^06 respectively but as a rule they are insignificant 

 because most of the thermometers function perfectly. 

 The differences are not systematic and therefore do not 

 influence the mean value of the difference. 



The results of this discussion are summarized be- 

 low: 



Source of 

 difference 



Thermometer 

 divided to 1/20° 



Proba- 

 ble 



Maxi- 

 mum 



Thermometer 

 divided to 1/10° 



Proba- 

 ble 



Maxi- 

 mum 



From this compilation it appears that for one compari- 

 son the probable difference between two thermometers 

 which both are divided to 1/20° is 0.°023 and on the av- 

 erage for a number of comparisons it is 0.°013 because 

 the errors of reading cancel. In order to find the range 

 over which the differences may be distributed we have to 

 take into account the maximum differences which may 

 result from errors of reading and errors of the breaking- 

 off device, considering that the errors due to limited ac- 

 curacy of test and from change in zero point are sys- 

 tematic. Assuming these differences to be negative we 

 find the limits -0.°068 to +0.°032, and assuming the dif- 

 ference to be positive we find the limits -0.°032 to 

 + 0.°068, and in both cases a range of 0.°100. This range 

 is reduced to 0.°020 if the breaking -off device functions 

 perfectly. The maximum value of the difference at one 

 single comparison is 01115 and the maximum average 

 value of many comparisons is 0.°066 with a range of 

 O.°100 as before. In case of the thermometers which are 



