The Hydrates of Hydrogen Bromide. Ill 



Taking a and c as each nearly 6, we should expect a priori 

 (according to the last paragraph but one) the probable error 

 between any two determinations of each coefficient to be about 

 2 ; and. a posteriori, we observe that of the six differences 

 presented by the four values of a, three are within and three 

 without 2/ A similar statement is true of the six values 

 of c. 



The precariousness of the results becomes much greater, 

 as the number of the variables is increased, as may be seen 



by considering the expression for -r- in the case of four, 



compared with that of three, variables. 



I do not think it necessary to exhibit the work in full. 

 What has been proved of arithmetical observations may be 

 true also of algebraic formulae — a better general result is 

 sometimes obtained by not working up all the particulars. 



To sum up : we have estimated the error incident to each 

 coefficient employed in determining the correlation between 

 organs. We have shown how this error becomes greater 

 with the number of the organs ; the instability of the con- 

 struction increases rapidly with its height. 



In reaching these conclusions respecting correlated averages, 

 we have come upon two principles of wider application. 

 (1) When observations are combined according to a system 

 of weights different from that which is known to be the best, 

 it is in general advantageous to reject a, certain class of the 

 given observations. 



(2) When, as usual, the observations range under a proba- 

 bility-curve, the median m corrected by the quartiles q { and 

 q 2 affords a formula for the Mean, viz. (l'2m + qi + q 2 )-^S'2 } 

 which is more accurate than that method of combining such 

 observations which has hitherto been supposed to be the most 

 accurate, viz. the Arithmetic Mean. The principle may be 

 applied with great ease and advantage to Discordant Obser- 

 vations *. 



IX. The Hydrates of Hydrogen Bromide. 

 By Spencer U. Pickering, F.E.S.f 



IN the various criticisms which have appeared in this 

 Magazine of the conclusions which I drew from my 

 study of the properties of sulphuric-acid solutions, no allusion 

 has been made to one of the strongest of the arguments 

 adduced in favour of the reality of the changes of curvature 



* See the papers by the present writer in the ' Philosophical Magazine ' 

 for 1886 and 1887. 



t Communicated by the Author, 



