The attack on Dr. Birkbeck is quite as personally concerned, undeserved. No one rancorous and as unjustifiable as most of the has been a greater friend to mechanics' informer ones have been from the same source. stitutions than Dr. Birkbeck, and more espeThey certainly are, as far as the doctor is cially to the one in London. METEOROLOGICAL RECORD, KEPT IN THE CITY OF NEW-YORK. Song Winter From the 26th day of March to the 29th of April, 1833, inclusive. [Communicated for the Mechanics' Magazine and Register of Inventions and Improvements,] Loader -moderately smoky, [or dry fog Saturday, 23-Do. of the ril 29th, 54. 25 inch. Average temperature of the week ending April 1st, 43.77.-Do. of the week ending April 8th, 52 week ending April 13th, 51.51.-Do. of the week ending April 22d, 53.62.-Do, of the week ending: Maximum of the barometer in March, on the 14th, 30.52-Minimun on the 25th, 29.57.-Rang The winds for the month of March were Northeasterly, including North, during 29 periods of o.rvation; Southeasterly, including E, 21; Southwesterly, including S, 49; and Northwesterly, including W, 47. The observations of the highest atmospheric currents, as indicated by the clouds during March 3 followsfrom the Northeastern quarter, 4; from the Southeastern, 4; from the Southwestern, 53; and from thorthwestern, 25. They helped every one his neighbor; and every one said to his brother, Be of good courage: so the carpenter encouraged the goldsmith, and he that smootheth with the hammer him that smote the anvil, saying, It is ready for the soldering; and he fastened it with nails that it should not be moved.—ISAIAH, chap. xii. ver. 6, 7. On the Methods of describing various Curves for Arches. By J. THOMSON, Civil Engineer, Nashville, Tenn. [From the American Journal of Science.] a-d uninformed in regard to the method of for seven centers c=3.229, and for nine finding the point D (fig. 1), or the distance centers c=3.242, and for eleven centers CD, the determination of which is the only c=3.251. Hence we have for difficulty he will encounter. The distance CD, in that communication, is only express. ed in indefinite parts, and not by means of a quantity derived from the ratio of A C to CB. In order to find CD, divide the difference of the rise and half span of the arch by the following decimal numbers: For five centers, divide by 0.794. For seven centers, 6 0.771. 6 0.758. 0.749. For eleven centers, The method of finding these divisors will be given hereafter. It may be observed that the last divisor is nearly 0.75, hence when eleven centers are used, multiply the above difference of rise and half span by 4, and divide by 3, the result will be the distance CD. Having found C D, make C H=3 C D. Take one from the number of centers to be used, and half the remainder will be the number of parts into which C H and CD are to be divided; CH into equal parts, and CD into unequal parts, increasing from D as 1, 2, 3, &c. Join these points of division, as in the figure, by straight lines, whose in. tersections will give the centers H, G, F, &c. Thus, when nine centers are used, as in the figure, CH is divided into four equal parts, and CD into the same number of unequal parts, increasing as 1, 2, 3, 4, from the point D. To find the above divisors, put CD=y, A Dr and the given quantities A C=a, and B C=d. Now when the number of centers is given, the broken line HD is equal to CD multiplied by a constant quantity; put this constant quantity =c, then H D=cy, and since the broken line A H must be equal to B H, we have x+cy=d+3y, whence a-d Five centers, CD=7 0.794 Seven centers, C D=7 Nine centers, C D= a-d 0.771 a-d 0.758 a- -d Eleven centers, C D= 0.749 Since it is thus almost as easy to trace an oval arch with nine or eleven centers as with three, the description of this arch by means of three centers ought always to be avoided, as it is not only disagreeable to the eye, but it is deficient in strength, in consequence of the sudden change of curvature resulting from this mode of description. Perhaps no curve unites beauty and strength in a greater degree than the cycloid. The arch, equilibrated by a horizontal roadway, is remarkable for strength, but it is deficient in beauty. The elliptic arch is per. haps the most graceful, but when the rise is small, compared with the span, it will not admit of great pressure with safety at the crown. The cycloidal arch, with the same rise and span with an elliptic arch, is more curved at the crown than the latter, and hence it will sustain a greater weight at that point, such as a heavy load passing over it. We are not at liberty, however, to choose the ratio between the rise and span of this arch, these being always to each other as the diameter of a circle to the circumference. The mechanical construction of the cy. cloid is very easy. The following method I have not seen noticed in any work on Me. chanics. Having fixed upon the dimension of the half span A C, (fig. 2,) take the rise BC such that A C will be to BC as half the circumference of a circle to the diameter, the lines F H and A E being parallel to each other, and perpendicular to A C, and make CH=C B. Let the describing line taken equal to B H or twice B C, be extended from H to A, and brought to a proper tension by means of the point or pin D. The curve A B is then described with the centers D and H. This curve will be an approximation to the cycloid. Fix a number of centers (the more the better) along the curve A B, and with these centers describe the curve B E, which will be a cycloid as near as can be obtained by any mechanical |