CITHAREXYLUM, Linn. RAUVOLFIA, Ruiz et Pavon. Syst. Linn. DIDYNAMIA ANGIOSPERMIA. Calyx campanulatus, 5-7-dentatus. Corolla calyce longior, tubulosa: limbo 5-lobo, patenti, suprà cum fauce densè barbato: lobis subæqualibus, retusis, æstivatione imbricatis. Stamina 5 v. 4, subæqualia, fauci inserta: filamenta brevissima, glabra: antheræ lineares, obtuse, biloculares: loculis internè longitudinaliter dehiscentibus, basi solutis, tandem subdivergentibus. Pistillum 1: ovarium 4-loculare: ovulis solitariis: stigma capitatum, minutè papillosum. Drupa dipyrena: nuculis osseis, bilocularibus, hinc convexis, sulcatis, inde planiusculis: loculis monospermis, basi interiore fossulâ cum stylo cummunicanti, substantiâ cellulosâ farctâ, instructis; testâ interiori membranaceâ, cellulosâ: albumen nullum. Embryo erectus, lacteus: cotyledones oblongæ, plano-convexæ: radiculâ inferâ, cylindraceâ, parùm attenuatâ, recta, cotyledonibus ter breviori. Arbores v. Frutices (Amer. Calid.). Ramuli sæpè abortivi, spinescentes. Folia opposita, indivisa. Petioli basi callosâ manifestè articulati. Flores terminales, racemosi v. solitarii. 1. C. flexuosum, spinosum; foliis elliptico-oblongis mucronulatis integerrimis subtus tomentosis, racemis paucifloris, calycibus 5-dentatis. Rauvolfia flexuosa, Ruiz et Pavon Fl. Peruv. et Chil. ii. p. 26. t. 152. f. a. Hab. in Peruvia fruticetis ad Huanuci urbem, et in Provinciis Huamalies et Tarmæ. Ruiz et Pavon. h. Vulgò Turucasa, i. e. spina obtusa. (V. s. sp. in Herb. Lamb.) Frutex biorgyalis, ramosissimus, spinosus. Folia pollicaria, v. sesquipollicaria, suprà rugosa. Flores parvi, ochroleuci, odore suavissimo. Drupa atropurpurea. 2. C. retusum, spinosum; foliis obovato-oblongis retusis integerrimis subtùs tomentosis, racemis paucifloris, calycibus 5-dentatis. Rauvolfia macrophylla, Ruiz et Pavon 1. c. 2. p. 26, t. 152. f. b. Hab. in Peruviæ collibus arenosis versus Atiquipa tractus. Joannes Tafalla h. Vulgò Chama et Spino de Cruzes. (V. s. sp. in Herb. Lamb.) Fruter biorgyalis, spinosus. Folia sesqui v. tripollicaria, rugosissima. Spine validiores. Racemi nunc multiflori. Flores lutescentes, majores. Drupa nigra. 3. C. dentatum, inerme; foliis obovato-oblongis dentatis glabris, racemis multifloris, calycibus angulatis multidentatis. Rauvolfia dentata, Tafalla MSS. Hab. in Peruviâ ad Maccos, 1794. Joannes Tafalla. h. (V. s. sp. in Frutex inermis, erectus, ramosissimus. Folia obovato-oblonga, den- 4. C. Lycioides, inerme; foliis lineari-lanceolatis obtusis integerrimis glabris, racemis paucifloris, calycibus integris. Rauvolfia sp. nova, Pavon. MSS. Hab. in Mexico. Sesse et Mocinno. h. (V. s. sp. in Herb. Lamb.) Frutex inermis, virgatus. Ramuli cortice cinereo-albicanti. Folia margine integerrima, parùm revoluta, vix uncialia. Drupa nigra. 5. C. lucidum, inerme; foliis elliptico-oblongis obtusis basi acutis utrinque glabris, spicis elongatis nutantibus. Citharexylum cinereum, Sesse et Mocinno MSS. non L. h. (V. s. sp. in Herb. Lamb.) subtùs reticulato-venosissima, apice Petioli unciales. Spica palmares. 6. C. Sessæi, inerme; foliis ovatis acuminatis subtùs pubescentibus, spicis elongatis nutantibus, ramis tetragonis. Citharexylum quadrangulare, Sesse et Mocinno MSS. Hab. in Mexico. Sesse et Mocinno. h. (V. s. sp. in Herb. Lamb.) 7. C. affine, inerme; foliis ovato-lanceolatis acutis membranaceis glabris, spicis elongatis nutantibus. Hab. in Mexico. Sesse et Mocinno. h. (V. s. sp. in Herb. Lamb.) Folia 2-4-uncialia, acuta, membranacea, glabra, basi acuta, pinnatè nervosa. Spice 5-pollicares, nutantes. 8. C. Mocinni, inerme; foliis ovato-lanceolatis acuminatis subtùs tomentosis basi rotundatis, spicis elonga.is pendulis. Citharexylum tomentosum, Sesse et Mocinno MSS. non Kunth. Hab. in Mexico. Sesse et Mocinno. h. (V. s. sp. in Herb. Lamb.) Folia ampla, ovato-lanceolata, acuminata, integerrima, coriacea, suprà glabra, nitida, subtùs ramulisque densè fulvescenti-tomentosa, dodrantalia. Spica tomentosa, pendulæ, pedales et ultrà. Calyx pentagonus: denticulis prominentibus. 9. C. scariosum, inerme; foliis ellipticis mucronatis coriaceis glabris, spicis erectis paniculatis. Citharexylum scariosum, Sesse et Mocinno MSS. Hab. in Mexico. Sesse et Mocinno. h. (V. s. sp. in Herb. Lamb.) Folia 2-3-pollicaria, venis prominulis. Petioli breves. Spica erecta, 3-5-unciales. 10. C. ellipticum, inerme; foliis subsessilibus obovatis oblongisve retusis mucronulatisque costatis scabris, spicis erectis multifloris, ramis tetragonis. Citharexylum ellipticum, Sesse et Mocinno MSS. Hab. in Mexico. Sesse et Mocinno. h. (V. s. sp. in Herb. Lamb.) 11. C. incanum, inerme; foliis ovatis serratis subtùs ramulisque pubescentibus, spicis erectis, dentibus calycinis inæqualibus. Citharexylum incanum, Sesse et Mocinno MSS. Hab. in Mexico. Sesse et Mocinno. h. (V. s. sp. in Herb. Lamb.) Folia ovata, acutiuscula, serrata, rarò subintegerrima, subtùs copiosè cinereo-pubescentia, basi attenuata. Petioli semunciales. Spica erectæ, sesqui v. tripollicares. Calyces 5-dentati: dentibus recurvis, inæqualibus; antico et postico majoribus. 12. C. scabrum, inerme; foliis ellipticis mucronulatis subtùs cinereo-tomentosis scabris, spicis erectis secundis, dentibus calycinis inæqualibus. Citharexylum scabrum, Sesse et Mocinno MSS. Hab. in Mexico. Sesse et Mocinno. h. (V. s. sp. in Herb. Lamb.) Folia 2-3-uncialia, suprà scabra, subtùs densè cinereo-pubescentia, basi acuta. Petioli semunciales. Spica erecta, 6-pollicares. Calyces 5-dentati: dentibus recurvis: antico productiore. On the adaptation of the Fly-wheel and Pulley of the Turninglathe to a given Length of Band. By Mr EDWARD SANG, Teacher of Mathematics, Edinburgh. EVERY one accustomed to the use of the turning-lathe, is aware of the necessity for frequent changes in the velocity of the spindle. Each different material that is wrought,—each diameter of the various parts of the work,-and almost every different tool that is employed to cut it,-requires a particular velocity. The most ready means for effecting these changes, is to cut two series of grooves, one series in the edge of the flywheel, and a corresponding one in that of the pulley; and to have these grooves so arranged that the same band may fit upon any one pair of them. When the band is crossed, the formation of these grooves is attended with no difficulty; for, while the sum of the diameters of the wheel and pulley is kept the same, the length of the band is unaltered. We have thus only to increase the diameter of the pulley as much as we diminish that of the fly-wheel; and it may be noticed, that the same band will pass over any pair of grooves formed agreeably to this rule, whatever be the thickness of that band. When the band is plain, the arrangement of the grooves is much more troublesome, and needs the aid of calculations too long and too intricate to be performed by the generality of those who are engaged in the construction of turning-lathes; on this account, the adjustment is most frequently effected after repeated trials. My object is to render these requisite calculations so simple as to offer no serious difficulty to practical men ; for this end, I will avoid every appeal to the complex operations of trigonometry, and will use such expressions only as may be intelligible in the workshop. By no artifice can the actual performance of the calculations be avoided; but, by entering the results in tables, the labour of one person may be made available to others. A complete Cable, to answer our present purpose, one which would only give to the artist the trouble of inspection, would need to exhibit the lengths of the bands which would pass over all pulleys and wheels placed at various distances from each other. The inconvenience attending all tables of triple entry, and the excessive labour of constructing such a one, forbid the hope of ever seeing it completed. Some mode must be devised which may abridge the labour of the calculator, without adding too much to that of the inspector; and I have now to explain those considerations which may be supposed to have led me to that abridgment which I have used: among these will be found all the principles which are necessary to the rightly understanding and using of the subjoined Table. When we have a table of the lengths of bands fitting on various wheels and pulleys, placed at one fixed distance from each other, it is not very difficult thence to compute the length of band for any lathe whose axes are placed at a different distance. Conceive all the parts of the lathe last mentioned to be altered in proportion, until the distance between its axes is equal to the distance between the axes of the former, and its parts will be found among those entered in the table. The length of band found for this size has only to be altered in the proper ratio, to give the length wanted, and the same might be said of any other dimension. Let the diameters of the wheel and pulley be equally increased: a little reflection will satisfy any one that the length of the band, the circumference of the wheel, and the circumference of the pulley will, all three, be equally increased; and that thus, as long as the difference between the diameters of the wheel and pulley is kept the same, the excess of the band above the circumference of the fly-wheel, as well as its excess above the circumference of the pulley, is also unchanged. Now it is an easy matter to compute the circumference of a wheel when its diameter is known; so that we require only a table of the excesses of the band above the circumference of the pulley, and above the circumference of the fly-wheel, corresponding to each difference between the diameters of these wheels. A table of these excesses, in the formation of which I took every precaution to insure accuracy, is subjoined. The first column contains the differences between the diameters of the fly-wheel and pulley, estimated in decimal parts of the distance between their axes, which is, throughout, regarded as the unit. In the second column, are inserted the corresponding excesses of the length of the band above that of the circumference of the pulley; these excesses being, for the sake of interpolation, accompanied by their differences. And the third column exhibits the excesses of the length of the band above the circumference of the fly-wheel, with their differences. The numbers in the first and second columns go on increasing, but those in the third column decrease. All the dimensions of any turning-lathe must be divided by the number which expresses the distance between the axes, before any of them can be sought for in this table; and the results obtained from the table must again be multiplied by the number formerly used as a divisor, in order to obtain the quantities sought for. But this calculation may be avoided, by forming a scale of the tenth, hundredth and thousandth parts of the distance between the axes, and by using this scale in all the measurements. The latter method will, in all probability, be found the most convenient. As examples of the use of the Table, I will propose two questions. I. On the pulley of a turning-lathe are already two grooves, one of 2.4, and the other of 5.0 inches diameter. The centre of the fly-wheel is distant 30 inches from that of the pulley, and the larger groove to be made on the fly is 25 inches in diameter. Required the diameter of the other groove to be made on the wheel? Dividing all these dimensions by 30, we obtain unit for the distance between the axes, which is the distance assumed in the table; 0.08 for the diameter of the lesser, 0.1666 for that of the greater groove on the pulley, and 0.833 for that of the greater groove on the fly-wheel. These numbers are just what would have been found on taking the dimensions with the scale above described. In order to find the length of the band, we take the difference between 0.8333 and 0.08, which is 0.75333, and enter, |