C. S. Peirce Manuscripts

5

to study these complicating operations, and to ascertain precisely what are the cases in which they are indispensible in proving a graph to be impossible, and to restrict their employment to these cases. This I have done. The operations of insertion and iteration receive their due recognition in Operation 5, while the useful effect of the operation of putting a double cut is fully attained in Operation 4. Namely, in case one has [a] [a b], one would insert a double cut round the right hand a thus, [a] [ a b ] and then, by deiteration, one would get [a] [ [ ] b ]. Arrived at this stage we put a double cut about b giving [a] [ [ ] b ] and by erasure [a] [ [ ] [ ] ] by deiteration [a] [ [ ] ] and removing the double cut [a]. But Operations 4 and 1 accomplish this and thus obviate the necessity of any