US532625A

US532625A - Apparatus foe harmonic analysis

Info

Publication number: US532625A
Authority: US
Publication date: 1895-01-15
Anticipated expiration: 1912-01-15

Description

2 Sheets-Shet 1.

(N0 Model.)

G U YULE APPARATUS FOR HARMONIG ANALYSIS.

,625. Patented Jan. 15, 1895.

(No Model.) 2 Sheets-Sheet 2.

G. U. YULE. APPARATUS FOR HARMONIG ANALYSIS. 625.

, P'atented Jan. 15, 1895.

TED' STATES PATENT OFFICE.

GEORGE IlDNY YULE, OF LONDON, ENGLAND.

APPARATUS FOR HARMONIC ANALYSIS.

SPECIFICATION forming part of Letters Patent No. 532,625, dated January 15, 1895.

Application filed September 8.1894. Serial N0- 522,498. (No model.)

subject of the Queen of Great Britain, residing at 40 Argyll Road, Kensington, in the city of London, England, have invented an Im-- proved Arrangement and Combination of Apparatus to be Employed in Harmonic Analysis, of which the following is a specification.

My invention is illustrated by the accompanying drawings, in which- Figure 1 is a plan of the combined appa ratus in a position it might assume in practice. Fig. 2 is a cross section of the rolling parallel ruler showing a rolling disk in use therewith, and Figs. 3 and 4. and Figs. 5 and 6 are respectively under side views and cross sections of other forms of rolling disks.

The theorem upon which my invention is based is that known as Fouriers, by which it is known that if y be a function of :20, y may be expanded in terms of sines and cosines of multiples of as, so that if :20 range from +n to 7r, we may write:

A,,:%] y sin me. do:

21r Bizfy cos. ma. dra

The following is a description of my improved apparatus and of the mode of using the same.

Let 0 P Q, Fig. 1, be the curve required to,

be analyzed. Let D be a disk whose circumference is equal to of O P (where n;1, 2, 3,

or 4:, &c.,) which is capable of rolling without slip along the edge L L of a parallel ruler or straight edge, the said ruler being necessarily of the character of a rolling parallel ruler, that is to say, a ruler only capable of such motion that every point in it describes a perpendicular to the line 0 P. Bring the center of the disk D over the point 0 and then carry it completely round the curve by moving the parallel ruler in the aforesaid manner and by rolling the disk D along its edge. Then it points A A of the disk, we shall have the comay be shown that any point A of the disk, initally'on its horizontal diameter atadistance r from the center, will describe a curve whose area is area of O Q P Oirw 1: A,

area of O Q P Oinr r: B

The sign or to be taken depends on the initial position of A or A to the right or left, above or below, the center of the disk. 0 may conveniently be made a multiple of The area of O Q P O, the original curve, will have been already determined in order to obtain A Consequently if we can determine the areas of the curves described by the GffiOlQlltS A, and B The following is a method of carrying the invention into effect:

L L isa bar of sheet brass or other metal with a fine rack out along its fore edge, and attached to the front of a rolling parallel ruler. D is a flat toothed wheel gearing into the rack. Its center may be given by an inserted disk at of glass marked on the under side with two lines at right angles, the continnations of the marked lines passing through or perpen dicularly under the points A A. As many such wheels or disks will be required as terms in the Fourier series, the numbers of teeth in them being in the ratios one, one-half, onethird, one-fourth, &c., and the largest-wheel having as many teeth as the length 0 P of the rack.

To obtain the area of the curve described by A or A, slight depressions may be formed at these points on the upper side of the wheel or disk. It now the tracer X of a planimeter X be allowed to rest in one of these depres- .sions- AA, .while the center of the disk is may be). As the tracer X of the planimeter will be raised above the surface of the paper on which the curve is drawn by this proceeding, it may be made adjustable vertically within its socket.

It may be desirable, especially in obtaining the coefiicients of the higher terms of the series, to bring the points A A outside the toothed wheel D. In this case a metal disk D is attached above the wheel D, as shown at Figs. 3 to 6, so as to sweep over the rack bar L L when the wheel D gears into it, and the depressions at A A maybe formed in the upper disk D.

I would here remark that the form of planimeter indicated in the drawings is that known as Amslers. I do not however confine myself to the use of such form of planimeter as other forms may also be employed.

Having fully described my invention, what I desire to claim and secure by Letters Patcut is 1. The improved apparatus to be employed in harmonic analysis consisting in the arrangement and combination of a parallel moving rack, a set of toothed disks, having centrally inserted glass disks marked with lines crossing each other at right angles to indicate the center, and having depressionsin the continuations of such cross lines to receive the tracer of the planimeter, and a planiineter, substantially as described.

2. The combination with a planimeter and a parallel ruler having a rack on its fore edge, of a set of toothed disks having centrally inserted glass disks marked with lines crossing each other at right angles to indicate the center, and having depressions in the continuations of such cross lines to receive the tracer of the planimeter, substantially as herein shown and described and for the purpose stated.

G. UDNY YULE.

Witnesses:

D. MICHAEL, JOHN C. BIGGAM, Both ofNat'rn, N B, Clerk-5' James Dunbar Lamb, Solicitor there.