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Rh 22 1915. He was succeeded in the baronetcy by his eldest son George (b. 1859), two other sons, Saxton (b. 1863) and John (b. 1865), becoming prominently associated as directors with the management of their father's great engineering firm of Armstrong, Whitworth & Co. of Newcastle. NOGI, MARESUKE [KITEN], COUNT (1840-1912), Japanese general (see 19.733). After the campaign of 1904-5 he was decorated with the Imperial Order of the Rising Sun with Paulownia and the first-class Military Order of the Golden Kite, in recognition of his distinguished services. He and Countess Nogi committed suicide on Sept. 13 1912, when the state funeral of the Emperor Mutsu Hito was taking place, in sign of their devotion to their imperial master. NOLHAC, PIERRE DE (1859- ), French scholar and author, was born at Ambert, Puy-de-D6me, Dec. 15 1859. He was educated at the lycees of Puy and Rodez, and afterwards studied at Clermont and in the ficole des Hautes Etudes at Paris. He entered the Bibliotheque Nationale in 1885, became professor of philology at the Ecole des Hautes Etudes in 1886, and was in 1892 made curator of the palace of Versailles, becoming hon. curator on resigning this post in 1921. He produced a series of works dealing with its history and associations, of which the chief are Le Musee National de Versailles (with A. Perate, 1896); Le Chdteau de Versailles sous Louis XV. (1898); Les Jardins de Versailles (1905); Histoire du Chdteau de Versailles (1911); Le Trianon de Marie Antoinette (1914) and Madame de Pompadour et des Arts (1920). His other works, which deal with a great variety of subjects, include Le Dernier Amour de Ronsard (1882); Lettres de Joachim du Bellay (1883); Erasme en Italic (1888); Petrarque et I'Humanisme (1892; new edition 1907); besides several volumes of poems, and works on Nattier, Fragonard, Hubert Robert, Boucher, and Madame Vigee-Le Brun. He was made an officer of the Legion of Honour.

See P. Bouchaud, Pierre de Nolhac et ses travaux (1896). NOMOGRAPHY. The methods of graphic calculation may be divided into two main groups, (a) Those in which a more or less complicated geometrical construction is performed for the solu- tion of an isolated problem. Graphic Statics (see 17.960) may be instanced as an example of this group, (b) Those in which all the solutions of a formula which are likely to be required are em- bodied in a permanent diagram with figured scales, drawn once for all, and read simply by the intersection of lines or the align- ment of points on it.

The methods grouped under (a) do not lend themselves readily to concise and useful generalization; they can in fact only be dealt with satisfactorily as they occur in direct connexion with a particu- lar subject. Those of group (b), however, the application of which in scientific and engineering work generally has developed consider- ably in recent years, can be successfully generalized, and they form the subject of this article.

It was M. d'Ocagne who, in his Nomographie: Les calculs usuels ejfectues au moyen des abaqucs (1891), invented the word Nomographie i.e. the graphical presentment of laws to describe the theory, and the word Nomogramme to describe the diagrams resulting from the application of these methods.

The English forms Nomography and Nomogram have now come into general use with similar meanings.

Although the invention and introduction of some of the methods utilized date back to a remote period, there can be no dispute as to the predominatingly important position to DC assigned to the work of d'Ocagne as far as the generalization and systematization of the modern treatment are concerned.

The exposition of the main principles given in this article follows the lines laid down in his works.

1. Notation. Following d'Ocagne the different variables appear- ing in an equation or formula will be denoted by Zi, z^, z 3. . . ., and the letters /, g, h, with appropriate subscripts, will be used to denote functions of these variables. Thus /i, gi, hi, will denote different functions of z\; / 2, g 2 , hi, different functions of Zj; / JS a function of Zj and Zj, and so on.

2. Graphic Representation. of a Two- Variable Formula in Car- tesian Coordinates. With the functional notation explained above, the most general expression for an equation connecting two vari- ables Zi, z--, is,

/u=o.

In the case of a practical formula, supposing z 2 to be the quantity which usually has to be determined for values of z\, we as a rule have the equation in the explicit form,

ZJ-/1-

Taking the rectangular axes Ox, Oy (fig. i) we construct the curve C, the " graph " of



the abscissa x and ordinate y of any point on this curve representing corresponding values of z\, Zj respectively.

Suitable scales are selected for z\ and z^, according to the size of the diagram and the range of values of z\, z 2 required.

Then, denoting by MI, f-t the units of the scales (zi), (zj),

define the graduations of the scales (zi), (z 2 ) along Ox, Oy.

If any two corresponding values of zi, Zj are taken and parallels to Ox, Oy drawn through the appropriate graduations on their respective scales, the intersection of these two straight lines gives a point on the curve.

Proceeding in this way with different corresponding values of Zi, Z 2, the necessary number of points on the curve to enable it to be constructed with sufficient accuracy are obtained.

Having constructed the curve in this manner, the value of z corresponding to any value of z\ is obtained by following the parallel to Oy through the given value of z\ on the scale (zi) till it cuts the curve, and then following the parallel to Ox through this point till it cuts the scale (zj) at a certain graduation. This graduation gives the value of z 2 required.

In order to save the trouble of having to draw the parallels on the diagram each time a reading is required, we construct a sufficient number once for all through the graduations of the scales (zi), (z 2 ) so that the eye can follow them and, if necessary, interpolate between them to read the corresponding values.

Looking at the matter in a slightly different way,

may be considered as defining two systems (Zi), (zi) of parallel straight lines at right-angles to each other, forming a rectangular network, the vertical and horizontal " meshes " of which are " fig- ured " to correspond with the graduations of the scales through which they are drawn.

For any two values of Zi, Zi which satisfy



we will then have two corresponding straight lines in this network which will intersect on the curve

amps

to p

T

In practice the familiar " squared paper," already prepared with rulings at intervals of a millimetre or a tenth of an inch, is largely employed for work of this sort. Fig. 2 shows such a diagram constructed for the electrical formula

giving the current (C) in amperes which will fuse a wire of diameter a mm., K being a constant depending on the metal of the wire. In this case the diagram has been constructed for lead wire (K = 10-8) of thickness up to I mm., and

Zi=d, Mi =50 mm.

Zj = C, M2 5 mm.

3. Graphic Representation of a Two- Variable Formula by Means of Two Adjacent Scales. The method described in 2 is the most