TRIPOS THOUGHTS.

(A long way after Swinburne.)

LIKE to the ghost of a gleam that gloats on the slumbering sea,

Like to the fall of a star or the flash of a flame ere

'tis spent ;

Like to the breath of the breeze that flits through the whispering tree,

Like to a whole host of things, (and I wish that I knew what they meant,)

Flashes the Tripos across me, the tyrannous turbulent Trip,

And, as it flashes, my brain reels, like a ship, 'neath the shock,

Reft of its ballast; and I must leave a short note for

my gyp,

And tell him, on pain of my wrath, to call me at seven o'clock.

Ere all the souls of the tired from dreamland's dim bourne have returned,

Ere the blithe cuckoo hath called o'er the long lush grass on the lea,

Ere the young Phoebus to fling his glistening glamour hath learned,

Ere e'en the milkman himself hath brought round the milk for my tea,

I must be up; woe is me, the load is so heavy to bear, The grim load of doubt and distress that on my sad

memory weighs;

Ah, why was not Pindar my pleasure, and Plato my loveliest care,

Why, with more pride than dismay, did I still get a Third in my Mays?

Ah woe, 'tis a quarter to nine, I wonder what fate will befall

Will some Special now be for me, will the General e'en be allowed?

Or shall I shine like a star, in the very first class of them

all?

Or (horrid thought) shall I be unutterably, hopelessly

ploughed ?

A. J. C.

A LETTER OF NEWTON'S.

RS. Adams has presented to the College, for the Library, a great literary treasure. It is an autograph letter, or rather a draft for a letter, in Newton's handwriting, which was given to the late Professor Adams by Sir David Brewster in 1855.

The text is as follows:

Sr,

I herewith send you the correction of the Moons Theory. The first half may stand as before, the latter half of it may run in these words:

{

Here a small diagram.

Dividi intelligatur distantia mediocris Lunæ a Terra in partes 100000, et referat T Terram et TC excentricitatem mediocrem Lunæ partium 5505. Producatur TC ad B ut sit CB sinus æquationis maximæ semestris 12 18' ad radium TC. Et circulus BDA centro C intervallo CB descriptus, erit Epicyclus ille in quo centrum Orbis Lunaris locatur et secundum ordinem literarum BDA revolvitur. Capiatur angulus BCD æqualis duplo argumento annuo, et erit CTD æquatio Apogæi, et TD excentricitas. Habitis autem Lunæ motu medio et Apogeo et excentricitate, ut et Orbis diametro transverso partium 200000; ex his eruetur verus Lunæ locus in Orbe, et distantia ejus a Terra, idque per methodos notissimas.

In periherio (sic) Terræ, propter majorem vim Solis, centrum Orbis Lunæ velocius movetur in epicyclo BDA circum centrum C quam in Aphelio, idque in triplicata ratione distantiæ Terræ a Sole inverse. Ob æquationem centri Solis in argumento annuo comprehensam, centrum Orbis Lunæ velocius movetur in Epicyclo illo in duplicata ratione distantiæ Terræ a Sole inverse,

ab Orbis centro D agatur recta DE versus Aphelium Lunæ seu recta TC parallela, et capiatur angulus EDF æqualis excessui Argumenti annui supra distantiam Aphelii Lunæ ab Aphelio Solis. Et sit DF ad DC ut dupla excentricitatis Orbis magni ad distantiam mediocrem Solis a Terra et motus medius diurnus Solis ab Aphelio Lunæ ad motum medium diurnum Solis, ab Aphelio proprio conjunctim, id est ut 33% ad 1000 & 52′ 27′′ 16′′ ad 59′ 8′′ 10" conjunctim, sive ut 3 ad 100. Et concipe centrum Orbis Lunæ locari in puncto F, et in circulo cujus centrum est punctum D et radius DF interea revolvi dum punctum D revolvitur circum centrum C.-Hac enim ratione velocitas qua centrum Orbis Lunæ circum centrum C movebitur, erit reciproce ut cubus distantiæ Solis a Terra ut oportet.

Computatio motus hujus difficilis est, sed facilior reddetur per approximationem sequentem. Si distantia mediocris Lunæ à Terra sit partium 100000 & excentricitas mediocris TC sit partium 5505 ut supra: recta CB vel CD invenietur partium 1172, et recta DF partium 35. Et hæc recta subtendit angulum ad Terram quam translatio centri Orbis Lunæ a loco D ad locum F generat, & cujus duplum propterea æquatio centri secunda'dici potest. Et hæc æquatio est ut sinus anguli quem recta illa DF cum recta a puncto F ad Lunam ducta continet quam proxime, & ubi maximus est, evadit 2′ 25′′ in mediocri distantia Lunæ a Terra. Angulus autem quem recta DF et recta a puncto F ad Lunam ducta comprehendunt, invenitur vel subducendo angulum EDF ab Anomalia media Lunæ vel addendo distantiam Lunæ a Sole ad distantiam Apogæi Lunæ ab Apogeo Solis. Et ut Radius est ad sinum anguli sic inventi ita 2' 25" sunt ad æquationem centri..[fragment missing] abducendam si summa illa sit minor semicirculo.. Sic habebitur locus Lunæ in Orbe, et per reductionem ad Eclipticam habebitur ejus Longitudo in ipsis Luminarium syzygiis.

Si computatio accuratior desideretur, secundi centri æquatio augeri potest vel diminui in ratione reciproca distantiæ Lunæ a Terra ad ejus distantiam mediocrem.

Si Longitudo Lunæ extra Syzygias desideretur, corrigendus est locus Lunæ in Orbe, ut supra inventus, per Variationem duplicem. De Variatione prima diximus supra. Hæc maxima est in Octantibus Lunæ. Variatio altera maxima est in Quadrantibus, & oritur a varia Solis actione in Orbem Lunæ pro

varia positione Aphelii Lunæ ad Solem. Computatur vero in hunc modum. Ut Radius ad sinum versum distantiæ Aphelii Lunæ a Perigæo Solis in consequentia, ita angulus quidam P ad quartum proportionalem. Et ut Radius ad sinum distantiæ Lunæ a Sole ita summa hujus quarti proportionalis et anguli cujusdam alterius Q ad Variationem secundam, subducendam si Lunæ lumen augetur, addendam si diminuitur. Sic habebitur locus verus Lunæ in Orbe: et per Reductionem loci hujus ad Eclipticam habebitur Longitudo Lunæ. Anguli vero P et Q ex observationibus determinandi sunt. Et interea, si pro angulo P usurpentur 2' & pro angulo Q 1' vel 1' 20", non multum errabitur.

Theoria Lunæ primo in syzygiis, deinde in Quadraturis & ultimo in Octantibus per phænomena examinari et stabiliri debet. Et opus hocce aggressurus motus medios Solis et Lunæ ad tempus meridianum in Observatorio regio Grenovicensi die ultimo mensis Decembris anni 1700 et veteri non incommode sequentis adhibebit, nempe motum medium Solis [Capricornus], 20. 23. 40, et Apogæi ejus v [Cancer] 7. 44. 30: Et motum medium Lunæ [Aquarius], 15.20.00, et Apogæi ejus [Pisces], 8.20.00, et Nodi ascendentis [Leo], 27.24.20: Et differentiam meridianorum Observatorii hujus et Observatorii Regii Parisiensis ohor. 9min. 20sec.

I have sent you this day by the Carrier Purver your MS wch Dr Bently left in my hands. I like it very well & think it deserves the light. I have sent you along wth it 32 wooden cutts done by Mr Livebody & amongst them there is a cut for this Theory of the Moon.

Mr R. A. Sampson, Fellow of the College and Isaac Newton Student of the University, has examined the manuscript. Though bearing neither signature nor date, it is undoubtedly Newton's; intrinsic evidence determines its identity and approximately its date. In 1709 Newton, who was then living in London, consented to the publication of a second edition of the Principia, which was then out of print and scarce, with Cotes, the Lucasian Professor, as editor. There followed a correspondence between Newton and Cotes, which lasted intermittently until the work was completed in 1713. This correspondence dealt with emendVOL. XVII.

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