Henry IV. Oliver Cromwell.

Henry V. Council of State and Parliament.

Henry VI. Charles I.

Edward IV. James I.

Edward V. ELIZABETH.

Richard III. MARY.

Henry VII. Edward VI.

Henry VIII. Henry VIII.

Edward VI. Henry VII.

MARY. Richard III.

ELIZABETH. Edward V.

James I. Edward IV.

Charles I. Henry VI.

Council of State and Parliament. Henry V.

Oliver Cromwell. Henry IV.

Richard Cromwell. Richard II.

Council of State and Parliament. Edward III.

Charles II. Edward II.

James II. Edward I.

William III. and Mary. Henry III.

ANNE. John.

George I. Richard I.

George II. Henry II.

George III. Stephen.

George IV. Henry I.

William IV. William II.

VICTORIA. William I.

NUMERIC THINKING.

HOW TO NEVER FORGET FIGURES AND DATES.

When my pupils have gained the quick perception and instantaneous apprehension which always reward the studious use of In., Ex., and Con., they can, amongst other new achievements, always remember and never forget figures and dates.

_Pike's Peak_, the most famous in the chain known as the Rocky Mountains in America, is fourteen thousand one hundred and forty-seven feet high.

Instantly, one who is trained in the use of In., Ex., and Con., perceives that there are two fourteens [Syn., In.] in these figures, and that the last figure is half of fourteen, or 7 In. by W. and P., making 14,147. Of course, one who is not practised in a.n.a.logies, in discovering similarities and finding differences would not have noticed any peculiarity in these figures which would enable him to remember them.

Few people ever notice any relations among numbers. But any possible figures or dates always possess relations to the mind trained in In., Ex., and Con.

_Fujiyama_, the noted volcano of j.a.pan, is twelve thousand three hundred and sixty-five feet high. Does any pupil who has mastered the first lesson and who is expert in the use of In., Ex., and Con., fail to notice that here we have the disguised statement that the height of this mountain is expressed in the number of months and days of the year, 12,365 feet high? These figures drop into that mould and henceforth are remembered without difficulty. These are remarkable coincidences no doubt, but are not all sets of figures similarly impressive coincidences to the trained eye, and the _active_, _thinking_ and _a.s.similative_ mind?

No reader of English history has failed to notice the three sixes in the date of the Great Fire in London, _viz._, 1666. The "three sixes" are generally resorted to as a signal for fire companies to turn out in full force; yet such a coincidence of figures in a distant date makes a slight impression compared to the vividness of events that happened in the year of our birth, the year of graduation from school, the year of marriage, and the year of the death of relatives, &c., &c. Keep a small blank book for such entries, not to help remember the dates or facts, but to have them together so as to rapidly deal with them, to cla.s.sify them and otherwise study them under the eye. You will soon be astonished at the acc.u.mulation.

The population of New Zealand, exclusive of natives, is 672,265.

Bringing the first two figures into relation with the last two we have 67 and 65--a difference of 2 only. The two groups of 672 and 265 have the figure 2 at the end of the first group, and another 2 at the beginning of the second group. These two twos are in sequence (Con.), and each of them expresses the difference between 67 and 65. _Thought_ about in this way, or in any other, the series becomes fixed in mind, and will be hard to forget.

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 circ.u.mstance that after considerable practice in dealing with numerous figures through In., Ex., and Con., new figures are self-remembered from the habit of a.s.similating 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 ant.i.thesis 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].

Haydn, the great composer, was born in 1732, and died in 1809; this date corresponds to that of the birth [Exclusion and Concurrence] of another famous composer [Inclusion], Mendelssohn, who himself died in 1847, the same year as O'Connell.

Lamarck [1744-1829], advocated a theory of development nearly resembling the Darwinian Theory of the Origin of Species [In.]. This he did in 1809, the year in which Charles Darwin was born [Con.]. Darwin's writings have altered the opinions of many as to the Creation, and the year of his birth was that of the death of Haydn, the composer of the Oratorio "The Creation." [Con. and Ex.].

John Baptiste Robinet taught the gradual development of all forms of existence from a single creative cause. He died in 1820, the year in which Herbert Spencer, the English Apostle of Evolution, was born [In., Ex., and Con.].

Galileo, founder of Modern Astronomy, born in 1564--Shakespeare's birth year [Con.]--died in 1642, the very year in which Sir Isaac Newton was born. Galileo's theory was not proved but merely made probable, until the existence of the laws of gravitation was established, and it was Newton who discovered gravitation. This is an instance of Inclusion as to the men, of Exclusion and Concurrence as to date of birth and death.

Two prominent _literati_ [Inclusion], one a Frenchman the other an Englishman [Exclusion], well-known for the pomposity and sonority of their style of writing [Inclusion], were born in the same year, 1709, and died the same year 1784, a double Concurrence--Lefranc de Pompignan--[pompous In. by S.], and Samuel Johnson.

General Foy, an _orator_ and artillery officer, fond of literature, was born the same year [Concurrence] 1775, as the _orator_ [Inclusion], Daniel O'Connell. He died in 1825, the same year [Concurrence] as Paul-Louis Courier, who was also an artillery officer [Inclusion], fond of literature [Inclusion], and moreover, like O'Connell, a violent pamphleteer [Inclusion].

Two ill.u.s.trious, uncompromising characters [Inclusion], both brilliant composers [Inclusion], the one musical, the other literary, the one a representative of the music of the future, the other of the obsolete polemic of the past [Exclusion], Richard Wagner and Louis Veuillot, were born in the same year, 1813, and died in the same year, 1883. The last point is a double Concurrence.

Two foremost harbingers of modern thought [Inclusion], Voltaire and J. J. Rousseau, died in 1778--[Concurrence]. Both gained for themselves the reputation of having been the most reckless antagonists of Christianity [Inclusion]. And still the one dedicated a church to the service of G.o.d, whilst the other in his "Emile" wrote a vindication of Christianity [Exclusion as to each of them, Inclusion as to both of them].

A little practice makes the pupil prompt in dealing with any figures whatever. Take the height of Mount Everest, which is 29,002 feet. We have all heard that it is more than five miles high. Let us test this statement. There are 5,280 feet in a mile, multiply 5,280 by 5, and we have 26,400. Hence we see that Mount Everest being 29,002 feet high must be more than five miles high. Half of a mile is 5,280 feet divided by 2, or 2,640 feet. Add this to 26,400 and we have 29,040. Hence we see that Mount Everest is 5 miles high lacking 38 feet, or that if we add 38 feet to its height of 29,002, it would then be exactly 5 miles high.

Can we then forget that it is exactly 29,002 feet high?

Shakespeare was born in 1564 and died in 1616. The First Folio Edition of his works was printed in 1623, the Second in 1632, the Third in 1664, and the Fourth in 1685. Can we fix these events infallibly in our memories? We can begin with whichever date we prefer. If we add together the figures of the year of his birth, 1564, they make 16. All the dates hereafter considered occurred in 1600, &c. We can thus disregard the first 16 and consider only the last two figures which const.i.tute the fraction of a century.

Let us begin with his death in 1616 in the _sixteens_. Is not this a vivid collocation of figures? Can we forget it as applied to the great dramatist? Now if we double the last 16, it gives us the date of the second Folio in [16]32 and 32 reversed gives us the date of the first Folio. Again, seven years after his death ["seven ages of man"] his first Folio was published in 1623. The second Folio was published in 1632 or 23 reversed, and the third Folio in 1664, or 32 doubled, and just 100 years after his birth in 1564. His birth might also be remembered as occurring in the same year as that of the great astronomer Galileo. The fourth Folio appeared in 1685 or 21 years after the third Folio. This period measures the years that bring man's majority or full age.

Attention to the facts of reading will be secured by increased power of Concentration, and a familiarity with In., Ex., and Con. will enable us to a.s.similate all dates and figures by numeric thinking with the greatest prompt.i.tude, especially the longer or larger series.

Try the case of Noah's Flood, 2348 B.C. Here the figures pa.s.s by a unit at a time from 2[3] to 4, and then by doubling the 4 we have the last figure 8--making altogether 2348. Another method of dealing with this date is very instructive. Read the account in Gen. ch. vii., vv. 9, 13, and 15. Now we can proceed.

They went into the Ark by _twos_. This gives the figure 2. Now let us find the other figures. Noah's three sons and their wives make three pairs of persons, or _three_ families. This gives the second figure 3.