1 873.] in Experimental Research. 11 



We have then, from the formula, — 



62 



The probable error = — , 



130^ 



62 



log. 62 — (log. 130 + log. 218) = 



130x218 



log. 0*0022, 



the number 0*0022 as the probable error. Or by means of 

 the tables calculated from the definite integral we can arrive 

 at a similar result. Thus — " What is the probability that 

 the truth is comprised within the limits a ± k ? " If k = o*oi ; 

 and 7r = H 



t = k Vw ; 

 then ^ = 47619, 



V w = 2l8 f 



t = k^w = 2'i8, and 

 tt=H 2 . i8 = 0-99795, 

 so near to unity, the measure of certainty, that the number 

 203*642 may, for all practical purposes, be regarded as the 

 absolute truth. From the second table we can also obtain 

 like results by entering with t. We obtain the argument 

 from the formula — 



k 



probable error 



= *. 



Therefore—^ =4'6 = t, to which corresponds £ = 0*00808. 



0*0022 *-* 



There can remain no reasonable doubt, then, that the atomic 

 weight of thallium is =203*642. 



As simply as I am able, I have endeavoured to show the 

 application of the theory of probabilities to the judgment of 

 error, and the evaluation of the amount of accuracy in experi- 

 mental research. The subject has, I think, been involved 

 with undue difficulty. Perhaps it has hitherto been gene- 

 rally held that the results of experimental research have not 

 been sufficiently accurate to permit the refinement ; but I 

 must express an opinion quite opposed. Yet I would suggest 

 that, in all kinds of delicate weighings, the effects of tem- 

 perature and pressure of the atmosphere be taken into 

 consideration. Let me make my meaning clear by an ex- 

 ample. There are given to be weighed, let us say, 800 grains 

 of water in 200 grains of glass. First arises the question, 

 —Shall we employ brass or platinum weights for our deter- 

 mination ? We shall presently see the difference that would 

 result, in the determination of the absolute weight of the 

 glass and water, from the result of our choice. A brass 



