SUBSURFACE TEMPERATURES 



differences are: (37339-514) = -0.°041 and (37339-127077) 

 = -0.°30. The first of these differences, -0.°041, cannot 

 be given any great weight because it is based on two 

 comparisons only. In these combinations thermometer 

 37339 is an old thermometer which was examined at 

 PTR in 1910 and re-examined in 1918 and 1922 to 1924. 

 On these three occasions the same correction at zero 

 was found. It should be expected, therefore, that 37339 

 gives correct temperatures. The results may be inter- 

 preted to mean that the two new thermometers, 514 and 

 127077, gave temperatures too high. Thermometer 

 37339 was used in combination with a third new ther- 

 mometer and the difference had the same sign also in 

 this case, namely, (339-127585) = -0.°016. Considering 

 that we should expect the zero point of the new thermom- 

 eter to rise, it is indeed probable that these gave tem- 

 peratures which were slightly too high when corrected 

 by means of the original PTR values and that the cor- 

 rections of the three thermometers 127077, 514, and 

 127585 actually should be lowered by about 0.°02 or 0.°03. 

 Another old thermometer, 67958, was used in combina- 

 tion with one of the new thermometers and the difference 

 was of the same sign as above, being (67958-127559) = 

 -0.°023. The correction of thermometer 127559 should 

 thus, perhaps, be lowered by 0.°02. We have no possibil- 

 ity of estimating the possible changes in all the other 

 thermometers, however, and it therefore seems inad- 

 visable to introduce any changes in these isolated cases, 

 especially since the mean differences always are based 

 on less than ten comparisons and therefore are uncer- 

 tain. Instead of changing the original PTR correction we 

 shall estimate, on the basis of the differences in tables 

 2, 3, and 4, the possible errors which are introduced by 

 retaining the PTR corrections. 



When discussing the probable differences between 

 two one-twentieth thermometers, it was found that this 

 difference, as a rule, is not greater than 0.°013. From 

 table 2 it Is seen that, omitting 908, the difference is 

 smaller than 0.°013 in fifteen of twenty-one cases and 

 that 'the greatest observed difference is 0.°025. The dif- 

 ferences in the change of zero point, thus, have not e;^- 

 ceeded 0.°025. The absolute change for each thermome- 

 ter is unknown, but on the average this change has prob- 

 ably amounted to -0.°015. Considering that it is not 

 probable that two thermometers have been combined 

 which have both changed appreciably, we can safely state 

 that the systematic error of the single thermometers, as 

 a rule, is smaller than 0.°02 and never greater thanO?03. 



The ranges over which the differences are distribu- 

 ted give an idea of the errors of reading and of the 

 breaking-off device and thus an idea of the error of one 

 single temperature determination. The maximum range 

 was estimated to 0.°100 and in case the breaking-off de- 

 vice always functioned perfectly we should expect the 

 range to remain smaller than 0.°020. We find that the 

 range is smaller than 0f020 in eight of twenty-one cases, 

 the maximum range being 0.°049. We therefore may 

 conclude that the errors of reading and of the breaking- 

 off device never exceeded 0.°03 and, since ths range is 

 smaller than 0.°031 in sixteen of twenty-two cases, that 

 the errors as a rule were smaller than 0.°015. The er- 

 ror of one single temperature determination by means 

 of these theremometers, therefore, is smaller generally 

 than 0.°035, ranging from -Of 005 to -0.^035, and the error 

 is in no case greater than +0.°06. 



Turning next to the thermometers which are divided 

 to 1/10° we find no greater scattering of the mean 



differences than in case of the one-twentieth thermometers 

 The probable mean difference between the one-tenth 

 thermometers was estimated to 0.°023 and the maximum 

 difference to 0.°160. We find a difference which is small- 

 er than 0.023 in twenty-nine of thirty-four cases, and a 

 maximum difference of 0.°030. Since the expected aver- 

 age change of the zero point for these thermometers is 

 -0.°02, we may safely state that the systematic error of 

 one single thermometer, as a rule, is smaller than 

 0.''025 and never exceeds 0f035. The ranges of the dif- 

 ferences are, as a rule, greater for these thermometers 

 than for the one-twentieth thermometers as should'be 

 expected because both the errors of reading and of the 

 breaking-off device inevitably are greater. The maxi- 

 mum range was estimated to 0.°160 and In case the 

 breaking-off device functioned perfectly, to 0.°040. We 

 find that the range is smaller than 0.°040 in twelve of 

 thirty-three cases and never greater than 0.°083. The 

 errors due to reading and breaking-off may, therefore, 

 reach 0.°05 but, as a rule, are considerably smaller than 

 0.°02. Thus the total error of one single temperature 

 determination is, as a rule, smaller than 0^045 and nev- 

 er greater than 0:°085. 



These conclusions are supported by an examination 

 of the cases in which a one-twentieth thermometer was 

 used simultaneously with a one-tenth thermometer. The 

 mean differences are of the same order as before and 

 do not exceed 0.°020, omitting thermometer 37339. The 

 ranges usually are greater than for the one-twentieth 

 thermometers but smaller than for the one-tenth ther- 

 mometers. If we subtract the corrected readings of the 

 one-twentieth thermometers from the corrected read- 

 ings of the one-tenth thermometers, we find a positive 

 difference in three and a negative difference in ten 

 cases, omitting thermometer 37339. The unweighted 

 mean difference Is -0.°0035. From this result it appears 

 that the corrections of the one-tenth thermometers have 

 not changed more than the corrections of the one-twentieth 

 thermometers. Since the corrected readings of the lat- 

 ter are slightly higher, the zero point of these thermom- 

 eters seems to have risen more than the zero point of 

 the one-tenth thermometers. It should thus be safe to 

 assume that the zero point of the one-tenth thermome- 

 ters has, as a rule, not risen more than Of025 and never 

 more than 0.°035. 



When discussing the possible differences, attention 

 was drawn to the circumstance that the differences be- 

 tween the two thermometers which were compared dur- 

 ing a long period should be expected to change, because 

 the changes of the zero points of the two thermometers 

 could not be assumed to follow each other. From table 

 4 It is seen that the differences between thermometers 

 127084 and 127088 and thermometers 127085 and 127086 

 have changed considerably, but the changes are In all 

 other cases small. A noteworthy change in the differ- 

 ence, therefore, seldom occurs. It was also mentioned 

 that older thermometers probably would give slightly 

 higher temperatures than more recently made thermom- 

 eters because the zero point of the former had risen 

 more. The cases in which a new thermometer was used 

 together with an older one are compiled in table 5. A 

 "new thermometer" is defined as one tested at PTR 

 less than eight months before its use and an "old ther- 

 mometer" is defined as one tested at least twelve 

 months earlier than a new one. The values given are 

 differences obtained by subtracting the reading of the 

 new thermometer from that of the old one. It is seen 



