fome of the first characters that ever graced Trinity College, were often heard to complain of.

To attempt in this effay, where I wish to be concife, to fay any thing on the fcience of Aftronomy, would be derogatory to its fublimity and usefulness: I have, therefore, only to remark, what a shameful hiatus in a literary character must even a fuperficial knowledge of this heavenly science be, acquired by dry lectures, and demonftrations for which the pupil is not prepared.

The myftic beauties of harmony are in a great measure loft to all but those who poffefs fufficient mathematical and philofophical knowledge to analyfe the conftructions of the piano-forte; organ; violin; guittar; monochord, &c. the propor tion of the founding ftrings, whether diatonic and of equal diameters, denfities, and tenfions, and the curve of the bridge of the piano-forte, and harpfichord, that of the conical hyperbola; or whether the ftrings, as now the cafe is, be metallic, and of different diameters, denfities and tenfions, and confequently the bridges, of other forts of curves.

Doctor Burney, in his hiftory of mufic, fays "all mathematical proofs, perhaps, are accidental coincidences, &c." It is to be wifhed this opinion, tho' delivered with a modeft diffidence which reflects honour on the doctor, may not deter those who are defirous to study the theory of mufic from fo delightful a purfuit. The opinions of the ancient philofophers and modern writers, on mufic, are decidedly against it. The feveral mathematical truths difcovered in the ancient diatonic fyftem, are too well known to require a comment. It must be acknowledged that the fefquialteral propofition of Archimedes, which may probably have given rife to the doctor's opinion, is an accidental coincidence, viz. An equilateral cone circumfcribing a fphere, a right cylinder circumfcribing the fame fphere; and the fame fphere continue the fame proportion of the key note; its fifth and the fifth to this fifth. This propofition put me on further pleafant enquiries of this nature, which follow, and are likewife accidental coincidences. The cylinder-its infcribed globeparabolic spindle-parabolic conoid and cone, continue the proportion of C—G— BThe octave to C, and G, in the next higher octave.

Thus, If the folidity of the cylinder be
That of the infcribed fphere will be

of the infcribed parabolic fpindle will be

of the infcribed parabolic conoid will be

And that of the infcribed cone will be

And if the length of the musical string to found the pitch note

or bafe C be

Then will the ftring to found G be

to found B be

to found the octave to C

to found G in the next higher octave

The difcovery made by Sir Ifaac Newton of the agreement of the intervals of the feven parent colours refracted by a prifm and feven notes in an octave, are admirable, tho' not, perhaps, accidental coincidences of nature difplayed in the analogy of the ffels of the degrees of refrangibility of a folar ray, and those of the vibrations of the mufical ftrings in an octave.

I here beg leave to advert to affertions of the ingenious MENTOR, in the Anthologia Hibernica for July 1794, and am forry to say that he totally misunder ftands when he fays" whence if the ray A B be expreffive of red, and performs two vibrations whilft C D performs one, and the latter will appear of an orange colour,

&c.'

&c." (page 52). Again, "whence the feven primitives being octaves, when placed by each other, have a pleasing gradation," (page 55). If the feven primitive colours are even admitted to be octaves, they cannot have the gradation hinted at. For the intervals of octaves, whether afcending or defcending, are all equal, in the ancient diatonic fyftem, which is that under confideration; but in order to refute this opinion, I fhall illuftrate the following beautiful difcovery of Newton. (See his Optics, page 111.) This incomparable mortal tells us, from the refult of feveral accurate experiments, that the interval of red is equal to

The difference of the intervals of the octave of the key note, and th minor. of orange equal to the difference of the intervals of

of the yellow equal to the difference of the inter

6th major and 7th minor.
vals of the 5th and 6th major.
of green equal to the difference of the intervals
major.

of the 4th minor and 5th
3d minor and 4th do.

of the tone major and 3d

of blue, equal to the difference of the intervals of

1

of indigo, equal to the difference of the intervals minor.

of violet equal to the difference of the intervals of the base C, or key, and tone major D.

ILLUSTRATION.

Suppofe the length of a monochord; or of the ftring to found the pitch note C of the ancient diatonic harpsichord, to be divided into 10,000 equal parts. Then will the length of the octave to C, be

That of the minor 7th or of

of the 6th major, or of }

of the 5th, or of

of 4th minor, or of 3

of 3d minor, or of

of the tone major of 3

of the bafe C or unity

Therefore-5625 -5000
6000 -5625
66663-6000
7500 66663

$333-7500 =

8888-8333

5000

And 10,000 88883—1111, that of the violet.

Sum of the intervals

5000, the interval of an octave.

Therefore the feven primitive colours are comprehended in one octave, and confequently cannot be octaves when placed by each other, as it here appears that their intervals differ very much.

Should there still remain a doubt of Newton's meaning, the following method of

finding

finding the ratios of the fines of refraction, I prefume will fully clear up this

Thefe are exactly the numbers determined by Sir Ifaac.

may

:

I shall conclude this difcourfe with the following remarks, which I flatter myself be acceptable to fuch of your correfpondents as have not read them before. Doctor Smyth of Trinity College, Cambridge (fee his preface to his Treatife on Harmonics)" Having been afked more than once whether an ear for mufic be neceffary to understand harmonics: It may not be amifs to give this answer. - A mufical ear is not neceffary to understand the philofophy of mufical founds, no more than the eye to understand that of colours: our late profeffor of mathematics was an inftance of the latter cafe, and the twentieth propofition of this treatise affords us an inftance of the former for by the folution of that propofition a person of no ear at all for mufic will foon learn to tune an organ, according to any propofed temperament of the fcale, and to any defired degree of exactness, far beyond what the fine ear, unaffifted by theory, can poffibly arrive at. And the fame perfon, if he pleases, may also learn the reafon of the practive" Monfieur Fontenelle, in his preface to the Memoirs of the Royal Academy at Paris, in the year 1699, "people very readily call ufelefs, what they do not understand. It is a fort of revenge; and as mathematics and natural philofophy are known but by few, they are generally looked upon as useless; the reason of this is, becaufe they are obfcure, and not cafily learned. A geometrical genius is not fo confined to geometry but that it may be capable of learning other sciences. A tract of morality, politics or criticifm; and even a piece of oratory, fuppofing the author qualified otherwife for thefe performances, fhall be the better for being compofed by a geometrician."

Pope Clement XIV. (Ganganelli) Vol. I, Letter LIX-" Mathematics will enable you to think juftly; without them there is a certain method wanting, which is neceffary to rectify our thoughts, to arrange our ideas, and determine our judgments aright. It is eafy to perceive in reading a book, even a moral one, whether the author be a mathematician or not. I am feldom deceived in this obfervation. The famous French metaphyfician would not have compofed The Enquiry after Truth; nor the famous Leibnitz his Theodice, if they had not been mathemati cians, We perceive in their productions that geometrical order which brings their reafonings into fmall compafs, while it gives them energy and method."

POETRY.