172 



NATURE 



{Dec. 26, 1878 



or mean tone temperament, a small semitone has 4I, a large one 

 7, and a tone 12 per cent, more vibrations. Tliese numbers are 

 very convenient for rou^h estimations. 



The old French foot is 6 per cent. longer than the English, 

 hence the one-foot pipe will be a semitone lower than the 

 English, or about 443 to 446 vibrations. I have not met with a 

 case of a French organ with A 443, or the one-foot pipe on A. 

 But Mersenne, 1636, places the one-foot pipe on G, and this 

 ■gives mean-tone A 496 and C 593. Now the St. Jacobi organ 

 had actually A 491 and C 584 (equal temperament, making the 

 C lower), as determined by forks tuned to the pitch and then 

 measu-red. Hence, Mersenne's pitch, which even M. Cavaille- 

 CoU considered mu;t be a mistake, actually exists at the present 

 day. 



2. The B flat foot organ, or B flat 472 to 475. This give^ 

 A 442, C 528, on the mean-tone temperament, that is, actually 

 the pitch desired by the Society of Arts and not attained. 

 This pitch was used by Thomas Harris in the Worcester 

 Cathedral organ of 1666, by Ber/iard Schmidt (or Father 

 Smith, as he has been called), in Durham Cathedral, 1683, 

 Hampton Court, 1690, St. Paul's Cathedral, 1694-7, Trinity 

 College, Cambridge, 1708, as I have ascertained, and probably 

 in all his organ?. It seems to have been occasionally used by 

 the yordans, who seem also to have built an A foot organ ; 

 but my inquiries are not yet complete. It is the favourite 

 pitch of modern English organ builders, as I have ascertained 

 by measuring the pitch-pipes of seven of the principal builders 

 in London, which vary from C 524 to 528, at 60° F., to which 

 all pitches are reduced. 



3. The B foot organ, or B472 to 475. This gives in 

 England A 422 to 425, and C506 to 512. This pitch was in 

 general use, from at least 1700 to 1820, over England and over 

 Germany. I found it in Renatus Harrises, All Hallows, Bark- 

 ing, 1675-7; St. Andrew Undershaft, 1696; and St. John's, 

 Clerkenwell (date unknown) ; in Harris and ByfieWs, St. 

 Mary's, Shrewsbury ; in Byjield, Jordan, and Bridge's two 

 Great Yarmouth organ=;, 1733-40; in Byfield and Green's, St. 

 Lawrence, Reading, 1771, and St. Mary's, Islington, 1772; in 

 Glyn and Parkei's, All Hallows the Great, Thames Street, 

 1749; in Schnetzler's, German Chapel Royal, St. James's Palace 

 (date uncertain) ; in Greenes, St. George's Chapel, Windsor, 

 1790; Will-Chester College Chapel, 1780; St. Katherine's, 

 Regent's Park, 1778 ; and Kew Parish Church (date unknown). 

 Glyn and Parker built the organ which Handel gave to the 

 Foundling Hospital, 1750, and Handel, after conducting a per- 

 formance of the "Messiah" there, in 1751, left his tuning-fork 

 behind him. This fork is now in the possession of Rev. G. T. 

 Driffield, Rector of Bow, and shows A 423, which is pre- 

 sumably the pitch of that organ. Mozart's clavier-maker. Stein, 

 at Vienna, 1780-90, used a fork one vibration lower, A 422, 

 which \\&s undoubtedly the pitch of Haydn and Beethoven, 

 and hence of Church music generally. It is a quarter of a tone 

 flatter than French pitch. This was the pitch used when the 

 Philharmonic Society was started in London, 18 13, and was 

 retained to 1826. Silbermann's organ at the Roman Catholic 

 Church, Dresden, w-as about a comma flatter, or A 415. 



4. The^C foot-organ, or C 472 to 475 and A 495. The only 

 instance known to me in England is Trinity College, Cambridge, 

 as recorded in 1759 by the celebrated Dr. Robert Smith, its 

 master, in his " Harmonics." But this was after its pitch 

 {which was originally that of a B flat foot-organ) had been 

 lowered a mean tone, by sliifting the pipes, which, as he tells 

 us, made it agree with the Roman pitch-pipes of 1702. But the 

 French foot being a semitone flatter than the English, the Ver- 

 sailles B foot-organ (1786) had a pitch of A 396, C 474, as 

 shown by the fork preserved in the Conservatoire in Paris, and 

 lience precisely agreed with the altered Trinity College organ 

 and the Roman pitch-pipe. Delezenne, in 1854, was fortunate 

 enough to find an old dilapidated organ at the Hospice Com- 

 tesse, near Lille, wliich gave C 448, as near as he could measure, 

 agreeing well with C 443, the calculated pitch of the French C 

 foot organ. 



Tliis seems to be the first attempt at systematically finding the 

 pitch of organs. The pitch of the pipes was in all cases fo'und, 

 when they could be actually heard, by beats with tuning-forks 

 made for me, to the extent of an octave, on the basis of Schei- 

 bler's 256, 435, 440 (which I have reason to believe perfectly 

 accurate), by Valantine and Carr, 76, Milton Street, Sheffield, 

 and I have also reason to believe that these latter forks are 

 not more than half a vibration wrong with Scheibler in any 



case. But before my complete paper is ready I shall have veri • 

 fied them by eighteen otlier forks of Scheibler now being very 

 carefully copied at Crefeld. To hear the beats I stand thirty or 

 forty feet away from the organ, and hold the fork over a re- 

 sonance jar tuned to its pitch by pouring in water. The bellows 

 is first filled, and no pumping is allowed during the ten seconds 

 that I count. The beats are beautifully distinct, and I consider 

 the result to be correct within one-fifth of a vibralion. 



The correction for temperature, which is most important (as 

 at C 500 it is more than half a vibration per degree Fahr. , to be 

 added for higher and subtracted for lower temperature), is found 

 by the following rule : — Add four per cent, to the number of 

 vibrations observed, divide result by 1,000, and multiply by the 

 number of degrees required. I have thus harmonised measure- 

 ments made between 73° and 45^^ F. 



The rule for finding pitch from measurement was given by M. 

 Cavaille-CoU (Camples Rendus, i86o, p. 176), and, reduced to 

 English measures, is as follows : — 



Let L be the length, in English inches, of an open flue 

 cylindrical metal diapason from the lower lip to the open end, 

 and D its internal diameter, also in inches. The latter measure 

 is frequently difficult to make, on account of the jagged, or 

 "coned," or compressed, extremity. Then use the outer cir- 

 cumference, by wrapping a piece of paper round the pipe where 

 it is truly circular ; calculate tlae diameter as -j'.j circumference, 

 and throw off -jV inch for the thickness of the pipe, to find D, 

 which has to be known with considerable accuracy. 



Let V be the number of double vibrations in the pipe, at 

 60° F., then 



20080 



I tried this formula with a whole octave of pipes at Green's 

 St. Katherine's organ, and found that the error rarely reached 

 one comma (or i in 80), which many persons can't hear, and 

 never reached two commas (or i in 40). Since a quarter of a 

 tone is 3 per cent, (or i in 33^), and a semitone is 6 per cent, (or I 

 in l6f ), this gives a far better knowledge than we can obtain by 

 ordinary estimation of ear, without counting beats by measured 

 forks. 



It would confer a great favour on me if any one could give 

 me these dimensions of old, unaltered organ jjipes for the pipe 

 which is nearest to twehe English inches in length, anywhere, 

 especially abroad, naming the place and the note, and, if pos- 

 sible, date and builder, or would point out any existing un- 

 altered old organs. Alexander J. Ellis 



25, Argyll Road, Kensington, W. 



The Formation of Mountains 



Mr. Alfred R. Wallace asks one of our "great" physicists 

 to enlighten us about the possibility of the interior of the globe 

 "cooling more rapidly than the crust." If he will turn to a 

 chapter on Conduction in such a work as Maxwell's " Theory of 

 Heat," he will find an explanation of the principle. At p. 

 247 is a passage especially relating to the loss of heat by the 

 earth. 



But perhaps even a little physicist may help our great naturalist 

 as the mouse did the lion. 



In the first place it is of course understood that whenever it is 

 said that " the interior of the globe cools more than the crust," 

 it is not meant that it ever becomes cooler than the crust, but 

 only that the interior, from age to age, goes on getting cooler 

 than it was before, whiLt the crust keeps at nearly a constant 

 temperature. 



An illustration, which I think gives a good idea of this process, 

 may be taken from the dispersion of a crowd of persons in the 

 street. Suppose each person to represent a certain quantity of 

 heat. Then the number of persons in any space may be con- 

 sidered to represent its temperature, so that the crowded part will 

 represent a very hot space. As the people disperse they move 

 off the more quickly the further they get from the dense mass.- 



Now draw two lines near together across the street at some 

 small distance from the densest part of the crov.d, and let the 

 space between these two lines represent the crust of the earth, 

 while the s' ace occupied by the crowd represents the earth's 

 interior, and' all beyond the outer line represents infinite space. 

 Then the number of people passing outwards betw een the two 

 lines at any particular moment will represent the quantity 

 of heat in, and so the temperature of, the crust. At the 



