Action of Heat on Potassic Chlorate and Perchlorate. 375 



the correction to be adopted. Deducting it from 58, or rather 

 58*5, we have 47*5, which is a very respectable approximation 

 to the real value, as it may be called, viz. 45. 



III. (3) Prof. Newcomb* soars high above the others, in 

 that he alone ascends to the philosophical, the utilitarian, 

 principles on which depends the whole art of reducing obser- 

 vations. Here are whole pages devoted to estimating and 

 minimizing the Evil incident to mal observation: With Gauss, 

 Prof. Newcomb assumesf " that the evil of an error is pro- 

 portional to the square of its magnitude." He would doubt- 

 less admit, with Grauss, that there is something arbitrary in 

 this assumption. Another somewhat hypothetical datum is 

 what he{ describes as the "distribution of precisions." In view 

 of this looseness in the data, it becomes a nice question 

 whether it is worth while expending much labour upon the 

 calculation. The answer to this question depends upon an 

 estimate of probability and utility, concerning which no one 

 is competent to express an opinion who has not, on the one 

 hand, a philosophical conception of the Theory of Errors, and, 

 on the other hand, a practical acquaintance with the art of 

 Astronomy. The double qualification is probably possessed 

 by none in a higher degree than by the distinguished astro- 

 nomer to whom we owe this method. 



IV. It remains to consider the fourth Method. But the 

 length and importance of this discussion will require another 

 paper. 



XL II. On the Action of Heat on Potassic Chlorate and Per- 

 chlorate. By Edmund J. Mills, D.Sc, F.R.S.^ 



IT has been pointed out by Teed||, and subsequently by 

 P. Frankland and Dingwalllf, that potassic chlorate and 

 perchlorate may be decomposed by heat in such a manner as 

 to lead in each case to various relations among the products 

 of decomposition. 



It has occurred to me that both of these chemical changes 

 are instances of Cumulative Resolution**, from which point 

 of view they admit of very simple, and at the same time 

 perfectly adequate, representation. 



* American Journal of Mathematics, vol. viii. No. 4. 

 t § 3, p. 348. % § 9, p. 359. 



§ Communicated by the Author. 



|| Proc. Chem. Soc. xii. p. 105 ; xvi. p. 141 ; xxxiii. pp. 24 & 25. 

 % Ibid. xvi. p. 141 ; xxxii. p. 14; and Trans. Chem. Soc. 1887, p. 274. 

 ** Phil. Mag. [5] iii. p. 492 (1877). 



