1878.] 



using the Balance with great delicacy, Sfc. 



11 



from slight differences of temperature of the two weights, and perhaps 

 from air currents caused by their motion inside the case. They do 

 not seem to be due to any fault in the clamping arrangement, since 

 that is employed equally in both, and the changing of the weights, if 

 effected gently, does not move the beam at all. 



When the deflection has been determined, it is multiplied by the 

 number of milligrammes corresponding to one scale division, and this, 

 of course, gives the difference between the weights. I have inter- 

 changed the weights in the two pans X and T, between the series of 

 weighings, in order to make the experiments like those conducted in 

 the weighings for the standard pound. But my object has not been 

 to show at all that the method gives consistent results day after day, 

 and, in fact, the difference between the weights has varied. For 

 instance, according to weighings I and II, A— B = "0446, while, 

 according to weighings III and. IV, A— B = '0232. There is a 

 greater difference between these than can be accounted for by errors 

 of experiment, and it probably arose from the small piece of wax with 

 which I made A nearly equal to B. The difference between the 

 weights when measured to such a degree of accuracy as that which I 

 have attempted, will, no doubt, vary from time to time, partly with 

 deposits of dust, partly with changes in the moisture in the atmo- 

 sphere, and so on. 



But I think the numbers which are given in the tables are sufficient 

 to show that the difference between two weights in any one series of 

 weighings can be measured with a greater degree of accuracy than 

 has hitherto been supposed possible. I give in the tables a full 

 account of the weighings, each series containing a determination of 

 the value of one scale division and a determination of the difference 

 between the weights. The greatest deviation of any one of a series 

 from the mean of that series of differences is always given. This 

 I consider a better test of accuracy of weighing than the probable 

 error. What is wanted in weighing is rather a method which will 

 give at once a good determination of the difference between two 

 weights. But I may state, that if the error of any one of a series be 

 taken as its difference from the mean of that series, the probable error 

 of a single determination of the difference between the weights in 

 the first four series is '4344 of a division, or '0054 mgm., that is, 

 8 4 oo wo^ - of the total weight, while the greatest error is 1*8 

 divisions, or "0224 mgm., that is 2 000^000 ^ °f ^ ne total weight. It 

 may be remarked that these weighings were all made during peculiarly 

 unfavourable weather when there were frequent heavy showers, 

 causing sudden changes of temperature, and thus seriously affecting 

 the working of the balance. In the series V — VIII the greatest error 

 is only toooVooo °^ the total weight, the weather having improved 

 considerably. 



