Proportional Representation. 43 



number of parcels making up exactly the number ap of 

 papers to be transferred ; but this will not always occur. 

 Let us suppose that, after taking as many parcels as possible, 

 as directed above, the parcel next in order is the parcel 

 APS: we have then to select the balance of the surplus, 

 aps suppose, from the parcel APS. 



We now repeat the process just gone through, i.e., we 

 break up the parcel APS into the smaller parcels A P S Q, 

 APSE,, &c. 3 A P SI, where, from what has gone before, 

 the notation will be obvious. Just as before, take as many 

 complete parcels as we can in the order indicated without 

 surpassing the number, aps, to be transferred. We can 

 continue this process until we either get the number of 

 papers we w r ant to transfer made up exactly by a number of 

 whole parcels, or until we exhaust the names of the 

 unelected candidates. In the latter event, the papers in the 

 parcel we have to select from are all exactly alike, if no 

 attention be paid to the names of elected candidates which 

 may be indicated on such papers. 



In all previous methods all such names are completely 

 ignored from this stage, so that the papers are, for all 

 purposes of this election, exactly alike. Hence we can pick 

 out exactly the number we want without exercising any 

 discretion. 



But in the method now proposed, as explained later 

 on, use may be made of the names of such elected candi- 

 dates. 



Hence, then, it is necessary to prescribe a further process 

 of selection. This process is exactly the same as that just 

 described, substituting names of elected candidates for 

 names of not-elected candidates. Thus, ignoring the names 

 of not-elected candidates, the parcel we have to select from 

 is broken up as follows : 



A B, A C, A D, . . . Al, 



and the rest of the process, being exactly similar to that 

 already given, need not be further described. 



This process can be continued, if necessary, until we have 

 exhausted the names of the elected candidates. We shall 

 then find that the papers in the parcel we have to select 

 from are al] exactly alike, except as regards the order in 

 which the names of the elected candidates are arranged 

 amongst the names of the not-elected candidates. 



Thus, writing down only the names of the indicated 



