On the Valuation of Life Contingencies. 39 



slags that were rich in oxide of iron gave by analysis — 



Iron 920 



Copper 2*4 



Sulphur .... 1-8 



Insoluble matter . . 1*4 



Nickel -3 



Manganese . . . trace 



Carbonaceous matters 1*3 



The slag obtained while making this iron was not exhausted of 

 oxide of iron, although three equivalents of lime for the silica 

 present were added as flux. Such iron is well-suited for the 

 precipitation of copper from solutions^ as described in a former 

 article^ and might be worth the attention of those who adopt 

 such processes. 



On the surface of slag we have occasionally met with a sili- 

 ceous froth of a gray- white colour, and very light, owing to its 

 porosity ; its composition was found by analysis to be — 



99-70 



In the black glassy slags we occasionally meet with large 

 pieces of a gray porous character resembling pumice, with an 

 appearance as if other substances had filtered out, leaving a ske- 

 leton of silica, heavier, more tenacious, and harder than the 

 froth referred to above. Its composition was — 



Silica 97-5 



Oxide of iron ... 1*0 



Sulphur . . . . ^8 



Lime '7 



iooFo 



[To be continued.] 



IX. On the Valuation of Life Contingencies by means of Tables 

 of Single and Joint Lives. By Charles James Hargreave, 

 Esq., LL,D., F.R.S.^ 



LET «i, a^. .an be the reciprocals of the roots of the expression 

 l—s^cc-\-s^^— . . +Sn-iX^~^ + SnX'^j which call 057. "We 

 have then cf>x=(l—a-i£c){l—a^x) . . . (1— ^^^.r), from which the 

 * Communicated by the Author. 



