an octave lower or more grave than the diapafon, are called fixteen 405 foot ftops; every note two octaves lower than the diapafon makes a thirty-two foot ftop; every note one octave higher than the diapafon makes a four foot ftop; two octaves higher, a two foot; three octaves higher, a one foot; and a twelfth higher, a three foot. Thefe denominations have been adopted according to the length of the largest pipe of fome ftops, in antient organs; but at prefent they denote only the above pitch of every ftop. According to them, one fays a trumpet of thirty-two foot, fixteen foot, eight foot, or four foot; inftead of a double double trumpet, double trumpet, trumpet, and clarion. Í thought it neceffary to give this little explanation of the above names of the ftops, on account of thofe readers who might meet with German treatises of mufic, where they are used. The names of every ftop in the large organ at Haerlem, according to the above defcriptions, fee in Dr. Burney's Prefent State of Mufic in Germany, &c. vol. ii. p. 306." P. 97.

P. 98. The ufe of pedals, and the defects to which a player is liable, who attempts to fupply their place by holding down a note with its fubfemitone, termed by Mr. K. a bus grace, are ingeniously demonftrated.

Ch. XII. P. 100. Of Style and National Music.—Mr. K. characterizes four styles of mufic; the church, chamber, theatre, and open field. Upon all of thefe, he makes useful and judicious remarks. The three great national styles are, according to Mr. K. the Italian, the German, and the French. We are forry to differ with fo learned a foreigner, when his small acquaintance with our English malters induces him to think, that we have made a mixture from the best compofers of all nations, who have refided among us, and not formed any style of our own. But from the days of Morley down to Purcell, and from Purcell to the prefent day, have we not had great and original compofers, whofe ftyle has been their own? Are not the works of Croft, Green, Nares, and Boyce, in the churchftyle, original? Are not the theatrical melodies of Arne, Howard, Arnold, Dibdin, and Shield, original? Are not the glees of Webbe, Stafford Smith, Stevens, and Callcott original? If these occafionally imitate other compofers (and doubtless many of them do) what fhall we fay to Handel? With an inexhaustless fund of invention and knowledge, he formally trod in the steps of a French compofer, and made his overtures generally on the precife model of thofe by Lulli; a flow movement, fugue and minuet. It is with great pleasure we learn, that Dr. Burney has been collecting dance-tunes, and national fongs, from all parts of the world; and we cordially unite with Mr. K. in the wifh that they may be foon given to Ff

BRIT. CRIT. VOL. XVII, APRIL, 1801.

the

the public. Mr. K. concludes his work with a fhort explana tion of the following pieces:

Allemande

Bouree

Courante

Loure

Paftorale

Sarabande

Chaconne

Thus terminate Mr. K.'s two Effays on the fcience of music in general; which, if they have been as productive of emolument,as they are deferving of encouragement, will no doubt appear again in a more convenient form, and become one large quarto volume, with the examples intermixed upon plates; as in Dr. Burney's, and Sir J. Hawkins's Hiftory. We fhould be happy to pay immediate attention to the new work of this author, Thorough Bafs, which has been lately published; but the prior claims of Mr. King and Mr. Shield demand our immediate notice and as we have much to lay before the public on both those useful works, particularly the latter, we fhall continue our observations in the fucceeding number.

upon

ART. IX. Tranfactions of the Royal Society of Edinburgh. Vol. V. Part I. 4to. 116 pp. 5s. 1799.

FIVE

IVE Papers form the contents of this publication; of the nature of which our readers will be informed in the following paragraphs.

I. Investigation of certain Theorems relating to the Figure of the Earth. By John Playfair, F. R. S. Edin. and Profeffor of Mathematics in the Univerfity of Edinburgh.

Notwithstanding the efforts of the greatest mathematicians, from the time in which Newton first demonstrated the fpheroidical figure of the earth, to the prefent day, the proportion between the polar and the equatorial diameters of the earth, has not yet been accurately determined; and, indeed, fome weighty obftacles feem to obftruct the way to the attainment of that object, at least beyond a certain limit.

The principal caufes which impede the accurate determination of that proportion, as Mr. Playfair juftly observes, are the local irregularities in the direction of gravity.

"Of thefe irregularities, that which arifes from the attraction of mountains has had its exiftence proved, and its quantity, in one cafe, afcertained, by the very accurate obfervations of the prefent Aftrono

mer

mer-Royal at Schehallien in Perthshire. We may trace the operation of this caufe in many of the degrees that have been actually measured. Thus, in the degree at Turin, when divided into two parts, and each eftimated feparately, that which was to the north of the city, and pointed toward Monte Rofa, the fecond of the Alps in elevation, and the first perhaps in magnitude; was found greater in proportion than that toward the fouth, the plummet having been attracted by the mountain above mentioned, and the zenith made of confequence to recede toward the fouth. There are no doubt fituations in which the meafurement of a small arch might, from a fimilar caufe, give the radius of curvature of the meridian infinite, or even negative.

"But there is another kind of local irregularity in the direction of gravity, that may alfo have had a great effet in difturbing the accuracy of the meafurement of degrees. The irregularity I mean is one arifing from the unequal density of the materials under and not fac from the furface of the earth; and this caufe of error is formidable, not only because it may go to a great extent, but because there is not any vifible mark by which its evidence can always be diftinguished. The difference between the primary and fecondary ftrata is probably one of the chief circumstances on which this inequality depends. The primary strata, efpecially if we include among them the granite, may often have three times the fpecific gravity of water, whereas the fecondary, fuch as the marly and argillaceous, frequently have not more than twice the fpecific gravity of that fluid. Suppofe, then, that a degree is measured in a country where the ftrata are all fecondary, and happens to terminate near the junction of thefe with the primitive or denfer ftrata, the line of which junction we fhall alfo fuppofe to lie nearly east and weft; the fuperior attraction of the denfer ftrata muft draw the plummet toward them, and make the zenith retire in the oppofite direction; thus diminishing the amplitude of the celestial arch, and increafing, of confequence, the geodetical meafute affigned to a degree. From fuppofitions, no way improbable, concerning the denfity and extent of fuch maffes of ftrata, I have found, that the errors, thus produced, may easily amount to ten or twelve feconds.

"While we continue to draw our conclufions, about the figure of the earth, from the measurement of fingle degrees, there appears to be no way of avoiding, or even of diminishing, the effects of these errors. But if the arches meafured are large, and confift each of feveral degrees, though there fhould be the fame error in determining their celefial amplitudes, the effect of that error, with refpect to the maghitude and figure of the earth, will become inconfiderable, being spread out over a greater interval; and it is, therefore, by the comparison of two fuch arches that the most accurate refult is likely to be obtained. But, in pursuing this method, fince the arches measured cannot be treated as fmall quantities, or mere fluxions of the earth's circumference, the calculation must be made by rules quite different from those that have been hitherto employed. These new rules are deduced from the following analyfis." P. 5.

It is not in our power to give our readers an idea of this ingenious analyfis, or of the rules which are derived therefrom, Ff2

without

without the diagram. The rules are clearly exemplified, and adapted to a variety of measurements. The method of carrying the approximation on to a great degree of accuracy, is likewife diftinctly pointed out; to which the following paragraphs are fubjoined.

"The fame thing that renders the comparison of large arches of the meridian useful for leffening the effect of errors arifing from irregularities in the direction of gravity, makes it ferve to diminish the

effect of all the errors of the aftronomical observations at the extremities of the arches, from whatever cause they arife. They are all diffufed over a greater interval, and have an effect proportionally less in diminishing the accuracy of the laft conclufion.

"The measurement therefore of large arches of the meridian, efpecially if performed in diftant countries, is likely to furnish the best data for afcertaining the true figure of the earth; and on this account extenfive and accurate furveys, fuch as that above-mentioned, are no lefs interefting to fcience, in general, than conducive to national utility. The furvey of this island, when completed, will furnish an arch of the meridian, beginning at the fame parallel where that measured in France terminates, and nearly of the fame extent, fo that the length of an arch of more than 16o, or almost a twentieth of the earth's circumference, will become known. The different portions of this arch compared with one another, or with the arch measured in Peru, will afford a variety of data for determining the true figure of the earth. "But furveys of the kind now referred to, afford likewise other materials from which the folution of this great geographical problem may be deduced. These are chiefly of two forts, viz. the magnitude of arches, either of the curves perpendicular to the meridian, or of the circles parallel to the equator. Examples of the first of these have been given by General Roy and Mr. Dalby; the observations which follow are directed toward both." P. 12.

But for those obfervations we must refer our readers to the paper itself, which is highly deserving of the attention of mathematicians.

II. Account of certain Phenomena obferved in the Air Vault of the Furnaces of the Devon Iron Works; together with fome practical Remarks on the Management of Bluft Furnaces. By Mr. Roebuck.

Thefe iron works are fituated on the banks of the river Devon, which runs into the Frith of Forth, three miles diftant from Alloa, and eight from Stirling.

An accurate defcription, accompanied with a fection of two blaft furnaces belonging to the above-mentioned works, form the beginning of the paper. Their conftruction is briefly as follows:

Two

Two large blaft furnaces are formed on a steep bank, by two pits funk in a very folid ftratum of coarse-grained freeftone. At the back of the two furnaces, next the bank, the air vault is excavated, and formed by a mine drove in the folid rock. This vault has an aperture at one end to receive the air from the blowing machine, which is actuated by a Newcomen's fire-engine; and has two apertures at the oppofite end, one of which receives the eduction pipe, and the other is a door to give admittance occafionally into the vault.

"As the rock is extremely clofe and folid, the vault is dry, except that a little water oozes very gently from the fide next the bank in fmall drops, and does not appear to exceed an English pint in 24 hours."

"When the furnace," fays this author, "was put in blaft, after having been filled with coakes, and gently heated for more than fix weeks, the keepers allowed it to have but little blast at first, giving it a fmall blow-pipe of about 24 inch diameter, and likewife letting off a very confiderable quantity of air, at the escape, or fafety valve on the top of the iron wind cheft, as it is a received though erroneous opinion among them, that the blast must be let on very gradually for fome months. From the conftruction of this valve, it was impoffible to afcertain the exact proportion of the blaft they thus parted with, but I believe it was very confiderable. The confequence was, that the furnace, after it had been in blast for several days, never feemed to arrive at its proper degree of heat, but was always black and cold about the tweer in the hearth, and appeared in danger of choking, or gobbing, as it is termed.

After various experiments tried in vain, by the keepers and the Company's engineer, and others, (indeed they tried every thing, except giving the furnace a greater quantity of air, which, as I afterwards afcertained, was all that it wanted) they concluded, that the air vault was the cause of the whole mifchief; and, to confirm their opinion, they faid they had now discovered that water was, in confideraable quantities, driven out of the air vault through the blow-pipe, which cooled the furnace; and they infifted, that the power of the engine was fuch as to force water out of the folid rock; so that this method of equalizing the blast never would fucceed. The other managing partner was fo much alarmed by these representations, that he began to confult with the engineer, and others, about finding a substi tute for the air vault at any expence.

"As the plan of the blowing apparatus had been adopted at my recommendation, and was now fo loudly condemned on account of the water, I had other motives, than mere intereft, for trying to become better acquainted with the phænomena attending it. Laccordingly determined to go into the air vault, and to remain inclosed in the condenfed air while the engine was blowing the furnace. It is an experiment that perhaps never was made before, as there never exifted fuch an opportunity. I could not perfuade the engineer, or any other of the operative people about the work, to be my companions, as they

imagined