Notices respecting New Books. 507 



partment full up to the height of the next compartment, as 

 shown by the dotted line in the figure ; and the rest of the 

 contents of the highest compartment massed at its left corner. 

 The quantity SOP 2 n is 



i(2x35'5) + f(31 + 25) + 2 ^xl3 + ^x4 + ^x-7=288. 



To this is to be added Sf JA (35*5 being substituted for h ) 



-A(Sfi-4-5)^A 145=12. 



Lastly, there is to be added the contribution of the upper 

 layer of the highest compartment on the most unfavourable 

 supposition ; =4*5. Thus the limit of the sum of the squares 

 of error is 305. This is to be divided by Sn for the modulus- 

 constant. The result is 2*04. This must be multiplied by 5 2 

 for the mean-square-of-error in terms of a single year ; and 

 again by 2 for the modulus-constant. The result is 102. By 

 a more accurate calculation, founded upon the discrete column 

 d x , from which the above data were compressed, I found for 

 the corresponding constant 90. We have therefore a very 

 serviceable approximation. The method may be extended to 

 cases where the facility- curve has more than one maximum. 



In conclusion, it may be observed that the procedure which 

 has been indicated is appropriate also to cases where a more 

 exact determination of the constant is theoretically possible. 

 The rough-and-ready method is sufficiently accurate for the 

 purposes of statistical induction. It is therefore the most 

 serviceable method whenever it is the most convenient. 



LXX. Notices respecting New Books. 



Select Methods in Chemical Analysis (chiefly Inorganic). By 

 William Ceookes, i^.i2.#., V.P. C.S. Second Edition. London: 

 Longmans, 1886. Demy 8vo ; pp. xxii and 725. 



IE it were allowable for a science to be provided with a motto, 

 " Crescit eundo " might well be that of Chemistry. In the 

 early years of this century, a single treatise of somewhat modest 

 dimensions was sufficiently large to " carry all we knew " ; but 

 modern chemistry has as many departments, and is as varied in 

 its applications, as modern mathematics. Two journals, indeed, 

 are devoted exclusively to analysis, — a department which also 

 occupies a prominent place in many others. 



The ' Chemical News,' of which Mr. Crookes is Editor, has for 

 many years past reserved a portion of its pages for abstracts of 

 papers in foreign chemical periodicals. These abstracts refer in 

 many cases to new or modified analytical methods ; and it for- 



