400 ME. J. J. MANLEY: OBSERVATIONS ON THE 



other lengthened. The imperfection may be removed by directing the screws along 

 lines which meet the sloping faces of the prisms at right angles, as shown in c. The 

 forces that the screws are called upon to resist then act along their axes, and there 

 will be no appreciable flexure. 



The simple method shown in d cannot be recommended. To be efficient and 

 trustworthy it demands that the prism shall exactly and rigidly fit the triangular 

 aperture prepared for it. It is unnecessary to dilate upon the difficulties inseparable 

 from such a scheme. We may, however, observe that, when we were using a balance 

 in which this mode (d) of attaching the knife-edges to the beam was adopted, 

 considerable irregularities in the R.P. curves were not infrequently exhibited. 



(4) Of the Effects produced by Variations in the Temperature of the Beam. 



We now proceed to examine the effects which may be produced by (l) slight 

 differences in the temperature of the two arms of the balance, and (2) a strictly 

 uniform increase or decrease in the temperature of the whole beam. 



(1) If the beam is of brass, we may assume a coefficient of expansion equal to 

 0'00002. Taking the length of eacli arm as 7 cm., we expect to have, at any uniform 

 temperature, 1 : 1 as the ratio between the two lengths. But if the temperature of 

 the one arm differs from that of the other by so much as 1/100 C., then the length of 

 the arm having the higher temperature will be 7'0000014 cm., and the new ratio 

 1 : 1 0000002. When using a sensitive balance under the conditions already described, 

 no difficulty would be experienced in detecting so small a change. This will be 

 apparent from the following example : The arms of a balance, the sensibility of which 

 was =70 for 1 mgr., were compared. Upon reversing the weights, the change in 

 the R.P. was found to be 42. The load in each pan was 200 gr. From these data 

 we find the ratio of the arms to be 1 : 1 '0000008. If the ratio had been 1 : 1 '0000002, 

 the total change in the R.P. would have approximated 10, a quantity which could 

 have been observed and measured with ease. 



If the balance is of the long beam type, a slight difference in the temperature of 

 the two arms would, in all probability, often exist ; for the longer the beam, the 

 greater will be the difficulty experienced in maintaining uniformity of temperature 

 within the case. 



These considerations led us to the inevitable conclusion that for weighings of the 

 highest degree of accuracy, the total mean difference between the temperature of each 

 arm must be much less than 1/100 C. 



(2) During this research it was observed that a balance, which was being kept 

 loaded for a lengthy period, gave different values for the K.P. from day to day. On 

 comparing these with the corresponding thermometer readings, it was discovered that 

 the variations were intimately connected with the rise and fall in the temperature. 

 The related changes in the R.P. and temperature are shown graphically in Fig. V. 

 Here the different positions of the curves evidently indicate a urn-directional 



