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Now let the pupil repeat from memory the series from George Washington to Andrew Jackson at least five times, each time recalling and realizing how each pair of names was linked together. After this let the list be recalled several times forward and backward, and more rapidly each time, without recalling the analysis.

REMARKS.

SECOND GROUP.

Two examples of In.: "An" and "Van", and "rew" and "Bu."

A good Inclusion occurs in the case of "ren" and "Hen." The name William belonged to no other of the twenty-four Presidents.

A fair example of In. by Sight is furnished by the syllables "ry" and "Ty."

The letter "l" belongs to both surnames but there is no other letter in common. John and James is a case of Con., for both occur together many times in the New Testament.

"K" is pronounced as if spelled "Kay," a good In. with "Tay."

The letters "ar" occur in both the Christian names.

The "an" in Franklin is identical in spelling and in sound with the two "ans" in Buchanan.

REMARKS.

THIRD GROUP.

The "l" in "coln," and the "h" in "John" are silent. It is a case of In. by sound. To the ear the sound of "Con." is like that of "Jon."

"An" in Andrew and in Grant has the same sound.

In "Gar" and "Ar" there is a strong In. by sound.

Between "thur" and "ver" there is a clear In. by sound.

There is a fair In. by sound between "an" and "am;" but as they are alphabetically reversed, it makes a case of Con. reversed.

Here "am" and "an" occur in alphabetical order, and is a case of In., and "jam," meaning pressing together, and "cleve" meaning to separate, are opposites, hence it is also an example of Exclusion.

Let the student, as in the case of the other groups, recall this list several times, and each time revive the relation by which each pair of names was cemented together, and after this let him recall this list several times both ways without reviving the cementing relations, and finally let him recall several times, both ways, the entire series of Presidents from Washington to Cleveland, and from Cleveland to Washington.

REMARKS.

ENGLISH SOVEREIGNS.

A UNIQUE EXERCISE.

We learn the order of the entire series of thirty-seven sovereigns by means of the relations, direct and indirect, which we establish with the reigning sovereign, Victoria.

No accidental relations of parts of names is resorted to, as was done in the case of the American Presidents.

The series is so taught that it can be recited forwards and backwards--the only true test of learning any series.

The series is completely worked out and nothing is left to chance or possible mistakes so liable to be committed by novices in dealing for the first time with a new process that has to be applied to many details.

Council of State and Parliament. Oliver Cromwell. Richard Cromwell. Council of State and Parliament.

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.

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 14 A.D.--End of Charlemagne's 814 A.D., and end of Napoleon's 1814 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 were born in the same year 1809 and died in the same year 1882 .

Garibaldi and Skobeleff , both great and recklessly patriotic generals and both favourites in France , died in the same year, 1882 . Longfellow and Rossetti, both English-speaking poets who had closely studied Dante died in the same year, 1882 .

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

Lamarck , advocated a theory of development nearly resembling the Darwinian Theory of the Origin of Species . This he did in 1809, the year in which Charles Darwin was born . 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." .

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 .

Galileo, founder of Modern Astronomy, born in 1564--Shakespeare's birth year --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 illustrious, uncompromising characters , both brilliant composers , 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 , 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 , Voltaire and J. J. Rousseau, died in 1778--. Both gained for themselves the reputation of having been the most reckless antagonists of Christianity . And still the one dedicated a church to the service of God, whilst the other in his "Emile" wrote a vindication of Christianity .

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 1/2 miles high lacking 38 feet, or that if we add 38 feet to its height of 29,002, it would then be exactly 5 1/2 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 constitute the fraction of a century.

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 assimilate all dates and figures by numeric thinking with the greatest promptitude, especially the longer or larger series.

Try the case of Noah's Flood, 2348 B.C. Here the figures pass by a unit at a time from 2 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.

A SCIENTIFIC EXPERIMENT.

I made the experiment two years ago, and all my experience since has corroborated the conclusion then arrived at.

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