160 REPORT — 1882. 



Column I. gives the principal points ; Columns II. and III. the 

 corrections according to Gay-Lussac's and Bessel's curves ; Columns IV". 

 and V. the mean excesses of the thread lengths, according as they are 

 corrected by one or the other curve ; Columns VI. and VII., the cor- 

 rections of the initial points themselves corrected by means of these 

 excesses. It will be observed that the differences are reduced, but as 

 the displacemeiit of each curve by the corrections is about the same, it 

 is difficult to say which is the more accurate between 100° and 110". 



Another point of divergence occurring about 135°, all the threads 

 whose ends fell on this part of the scale were picked out, thirteen in, 

 number. Their differences from the means, expressed in thousandths, 

 were, in the case of Bessel's curve, 



0, 0, -1, 6, 1, -1, 5, 4, 0, -4, -2, -G, 2; total 4, 

 and in the case of Gay-Lussac's curve, 



4, 3, -1, 5, 1, 2, 1, 8, 2, 0, 1, -3, 8 ; total 31. 



This shows that the lengths given by the Gay-Lussac curve are on 

 the whole too great, or that in this part it lies too high, and is the less 

 accurate. On the whole, then, the Bessel curve seems to be the best, as 

 theory would indicate. The extreme difficulty of obtaining an agreement 

 throughout to less than 0°-005 is, however, shown by the discrepancies 

 between the numbers given by Bessel's and Thiesen's methods. The 

 probable error of a thread measurement is, according to the number given 

 by Bessel's curve, 0°0025. Hence the probable error of a correction 

 ought, according to Table IV., to be about 0°-0008 and 0°-001, according 

 as it was determined by Bessel's or Thiesen's methods. They differ, 

 however, in several places by 0°-005, and each receives independent con- 

 firmation from one of the other methods. 



(18) The agreement in Table V. will or will not be considered good 

 according to the standard of accuracy to which the readings of the 

 thermometer, when in actual use, attain. 



Two members of the Committee (Professors Thorpe and Riicker) have 

 frequently had occasion to read the same thermometer together, and they 

 always agree to O^-Ol (O'l m.m.). This indicates a possible reading error 

 of -4- 0°-005 (005 m.m.), when no lens or other aid is used. Pernet 

 has~however, come to the conclusion that the distance between the fixed 

 points can be determined to 0°-001, and thus Miirek and others think that 

 a thermometer should be calibrated to 0°-002 at least. It may there- 

 fore be convenient to lay down three standards of accuracy, defined by 

 the conditions that the differences between the corrected and the true 

 scales shall not exceed 0°-l m.m. (0°'01 in Thermometer C) in the first, 

 0°-05 m.m. in the second, and 0°-02 m.m. in the third. 



(19) The observations on the Kew thei-mometers show that the first 

 standard can be reached by a calibration conducted after Welsh's method 

 with a good dividing engine. Inasmuch as the two Gay-Lussac curves 

 shown in fio-. 1, Plate I., nowhere differ by more than 0°-12 m.m. 

 (0°-011), except at the point 135°, where the difference could no doubt be 

 reduced by a subsidiary correction near that point, the first standard is 

 certainly attainable by a single Gay-Lussac correction conducted with a 

 short thread and with Mr. Brown's instrument, provided that special 

 attention be paid to the accurate investigation of maxima and minima. 



The second standard can be obtained with Mr. Brown's instrument 



