The population of Sydney is 386,400. Here are two groups of three figures each. The first two figures of the first group are 38, and the first two figures of the second group are 40—a difference of 2. Two taken from 8 leaves 6, or the third figure of the first group, and 2 added to the first figure of the second group makes 6. The 40 ends with a cypher, and it is a case of Syn. In. that the last figure of the second group or the third figure of it should likewise be a cypher. Besides, those who know anything at all about the population of Sydney must know that it is vastly more than 38,640, and hence that there must be another cypher after 40, making the total of 386,400.
The population of Melbourne is 490,912. Here we have 4 at the beginning and half of 4 or 2 at the end of the six figures. The four interior figures, viz., 9091 is a clear case of Con.—or 90 and 91. Then again 91 ending with 1, the next figure is 2—a case of sequence or Con. But 490,912 is the population of the city of Melbourne with its suburbs. The “city” itself contains only 73,361 inhabitants, 73 reversed becomes 37—or only 1 more than 36. This 1 placed at the end of or after 36 makes the 361. Now 37 reversed is 73, and then follows 361, making the total to be 73,361.
Let the attentive pupil observe that this method does not give any set of rules for thinking in the same manner in regard to different sets or example of numbers. That would be impossible. Thinking or finding relations amongst the objects of thought must be differently worked out in each case, since the figures themselves are differently grouped.
The foregoing cases in regard to population will suffice for those who live in the Australian colonies, and to others they will teach the method of handling such cases, and leave them the pleasure of working out the process in regard to the population where they reside, or other application of the method they may wish to make.
Great encouragement is found in the circumstance that after considerable practice in dealing with numerous figures through In., Ex., and Con., new figures are self-remembered from the habit of assimilating numbers. They henceforth make more vivid impressions than formerly.
Inclusion embraces cases where the same kind of facts or the principles were involved, or the same figures occur in different dates with regard to somewhat parallel facts—End of Augustus’s empire [death] 14 A.D.—End of Charlemagne’s [death] 814 A.D., and end of Napoleon’s [abdication] 1814 A.D.
Exclusion implies facts from the opposite sides relating to the same events, conspicuously opposite views held by the same man at different periods, or by different men who were noticeably similar in some other respects, or antithesis as to the character or difference in the nationality [if the two nations are frequent foes] of different men in whose careers, date of birth, or what not, there was something distinctly parallel—Egbert, first King of England, died 837. William IV., last King of England, died 1837. What a vivid exclusion here for instance: Abraham died 1821 B.C., and Napoleon Bonaparte died 1821 A.D.
Concurrences are found in events that occur on the same date or nearly so, or follow each other somewhat closely.
Charles Darwin, who advocated evolution, now popular with scientists in every quarter of the globe, and Sir H. Cole, who first advocated International Exhibitions, now popular in every part of the world [Inclusion] were born in the same year 1809 [Concurrence] and died in the same year 1882 [Concurrence].
Garibaldi [the Italian] and Skobeleff [the Russian] [Exclusion, being of different countries], both great and recklessly patriotic generals [Inclusion] and both favourites in France [Inclusion], died in the same year, 1882 [Concurrence]. Longfellow and Rossetti, both English-speaking poets [Inclusion] who had closely studied Dante [Inclusion] died in the same year, 1882 [Concurrence].