.ON A QUARTZ THREAD GRAVITY BALANCIi. 241 



The adequacy of the temperature observation, and of the instrumental adjustments, 

 will now be discussed. 



Temperature Corrections. Any given temperature measurement is clearly affected 

 with the sums of the errors of the coils employed. The accuracy with which the 

 coils are compared with each other and the bridge wire is chiefly a matter of 

 galvanometry. We made our comparisons with the galvanometer used in the tem- 

 perature observations, and, consequently, cannot hope to attain the highest possible 

 accuracy of which the method is capable. A long series of comparisons shows that 

 the working accuracy, or rather consistency, attained in the temperature measure- 

 ments is within 0'01. If we suppose that any observation is in error by this amount, 

 the resulting uncertainty may be stated as 0'3 minute (sextant). This would lead to 

 an error in the estimation of the value of g of one part in 700,000 very nearly. 



Accuracy of Setting on the Lever and Reading the Circle. The position of the 

 vernier arm can be read to 10 seconds of the graduation of the arc, or to 5 seconds 

 of arc. The magnification of the microscope is such that if we move the vernier arm 

 through 10 seconds (sextant), the end of the lever is displaced on the cross wires by 

 a comparatively large amount an amount two or three times larger than the least we 

 could see. We may say then, that the accuracy of setting is such that we are not 

 affected with any errors on this score comparable with those which occur in reading 

 the vernier. With regard to the latter we will suppose that, taking the sensitive- 

 ness as before, an error of 10 seconds in reading the vernier arm would lead to an error 

 in the estimation of g of one part in 1,300,000. This is about half the temperature 

 error. 



Errors of Levelling. The indications of the instrument depend on the assumption 

 that the line of collimation of the microscope can be brought to the same position 

 with respect to the horizontal at each observation. We have already discussed the 

 precautions taken to insure this being the case ; but, as there pointed out, there is a 

 certain outstanding theoretical uncertainty on this score, and, moreover, there is no way 

 of applying a check. Setting this aside, we consider that the axis of the microscope 

 tube occupies the same relative jxwitibn with respect to the horizontal plane whenever 

 the level reverses. The readings of the position of the ends of the bubble can be 

 got with certainty to within 0*2 of a division. It is not always possible to adjust 

 the level during an observation so that the bubble occupies its reversing position. 

 In practice our observations have been made with the maximum error of 0'6 in the 

 position of the bubble. By trial, we have found that if we displace the bubble 

 by 9'0 divisions we alter the circle reading by 150 sextant minutes. It follows that 

 an error of levelling of one division of the level scale would introduce an error of 

 0'3 sextant minute, or one part in 700,000 in the value of g. 



If all these three maximum errors conspire, we shall obtain a value of g in error by 

 one part in about 300,000. It must not be forgotten, however, that with the exception 



VOL. CXCIII. A. 2 I 



