1873 •] i n Experimental Research. 7 



before, the probability will be determined by the given 

 formula. 



If k= O'lOO, 

 •^ = 25*200, 



^w= 5*020, 



t= 0-502, 



7T=H - 5 o2 = 0*52. 



This result, 0*52, is just intermediate between unity or 

 certainty and zero, the lowest degree of probability, other- 

 wise denominated impossibility. Hence, that the true 

 number is within the limits stated is just as likely as the 

 throwing of Head with a single halfpenny, but not more 

 likely. 



I will now submit a practical application to the reader. 



The value of the results obtained during any series of ex- 

 periments must of course vary with the care taken in the 

 performance of the individual experiments. In support of 

 this view I have, in the practical application of the laws I 

 here endeavour to simplify, taken the utmost pains to 

 ensure accuracy. The application is the determination of 

 the atomic weight of thallium ; and I shall first enumerate 

 the means (not usually employed) by which I deem accuracy 

 to have been ensured, and then proceed to evolve the results. 



With a metal of so high an atomic weight (203*642) as 

 thallium, errors and inaccuracies comparatively trivial 

 with elements of low atomic weight, are magnified into 

 alarming prpportions. Impurity of the reagents employed, 

 imperfect manipulation, but, more than any, the inaccuracies 

 arising during the weighing from the omission of the cor- 

 rections required by temperature, pressure, &c, — all these 

 influences must be eliminated in the determination of an 

 atomic weight. 



The atomic weight was derived by two methods : — First, 

 by taking a known quantity of metallic thallium, dissolving 

 it in nitric acid, and weighing the nitrate of thallium pro- 

 duced. Secondly, in dissolving known quantities of sulphate 

 of thallium in water, and ascertaining how much nitrate of 

 barium is necessary to precipitate the sulphuric acid as 

 sulphate of barium. 



There were also two methods of weighing : one in air, at 

 ordinary pressure and temperature, and one in a highly 

 rarefied atmosphere. For the first method a balance was 

 employed, made expressly for the work by Messrs. Keissler 

 and Neu, which will indicate clearly a difference of o'oooi 

 of a grain when loaded with 1000 grains in each pan. For 

 the second method of weighing a balance was employed 



