8 Mr. T. Weddle on Annuities and Assurances 



mineral ackl, a copious precipitation of dark-coloured matter 

 takes place, which is doubtless AgS. But whether the whole 

 of the silver is precipitated under these circumstances as sul- 

 phuret I did not ascertain ; though from the copious precipi- 

 tate produced, I think that such is probably the case. 



Concluding Observations. 



1 . The loss of fine silver in the most satisfactory experi- 

 ment was 13i per cent. Formerly, in the old amalgamation 

 process in Mexico, my respected friend Mr. John Taylor in- 

 forms me, the loss frequently amounted to 35 per cent. But at 

 present, since the introduction of the barrel-process, the loss 

 has been reduced to 9 or even 5 per cent. My results there- 

 fore may be regarded as sufficiently satisfactory to justify at- 

 tention to them with reference to their oeconomic application. 

 It is probable that on the large scale, with proper appliances, 

 the silver would be much more completely extracted. 



2. I would especially direct attention to chloride of lime 

 and chlorine as the agents for effecting the conversion of the 

 silver into chloride, and to hyposulphite of lime, which may 

 readily be obtained as a cheap substitute for hyposulphite of 

 soda to dissolve the chloride. The silver it is obvious might 

 be precipitated either as metal or sulphuret. 



3. Since many of the South American silver ores contain 

 gold, it is desirable that both the silver and gold should be 

 extracted by one process ; and to this end chlorine or chloride 

 of lime seems to be indicated by the preceding experiments. 



II. On Annuities and Assurances on Successive Lives, 

 By Thomas Weddle, F.R.A.S.^ 



MILNE, in his Treatise on Annuities (Chapter VII.), has 

 discussed this subject with much clearness and elegance; 

 yet his method of investigation does not seem to be the best 

 possible, nor do I think that his results are given in forms 

 well adapted to numerical applications. It may therefore be 

 not altogether useless to consider the subject in a somewhat 

 different manner, and so to exhibit the formulas as best to 

 meet the wants of the computer. 



Problem I. To determine the present value (a„) of an 

 assurance oi £\ payable on the failure of the last of ti success- 

 ive lives A', A" .... A^''^ 



Let a<^^^ denote the value at the time of nomination of an 

 assurance of £l payable on the death of A^^^; A^^^ itself de- 

 * Communicated by the Author. 



