Treatise on natural philosophy . susual. It shotild be noticed that this solution fails for the case ol ^ = \ (it +1) v. 707.] STATICS. 253 Or when it is best to have the result in series of sines ofRectaneie ea multiples of ir^a, we may take M = 1(7 + 1-1. -xl /K^\ • ^^^ ^^ A which, with (54), gives -3-j+ —— = 0. .(66), boundea bytwo con-centric arcsand tworadiL and leaves, as boundary- conditions in the solution for to, 2a w zlA = \Ta- Y^-\-^- -k\ when ^7 = 0, and when i7 = /3, , _ . ana w = 0 when ^=0, and when |=a. The last shows that the A^ and A^ part of (58) is proper for to,and the two
Treatise on natural philosophy . susual. It shotild be noticed that this solution fails for the case ol ^ = \ (it +1) v. 707.] STATICS. 253 Or when it is best to have the result in series of sines ofRectaneie ea multiples of ir^a, we may take M = 1(7 + 1-1. -xl /K^\ • ^^^ ^^ A which, with (54), gives -3-j+ —— = 0. .(66), boundea bytwo con-centric arcsand tworadiL and leaves, as boundary- conditions in the solution for to, 2a w zlA = \Ta- Y^-\-^- -k\ when ^7 = 0, and when i7 = /3, , _ . ana w = 0 when ^=0, and when |=a. The last shows that the A^ and A^ part of (58) is proper for to,and the two first determine A^, A^. 708. St Venants treatise abounds in beautiful and instruc-tive graphical illustrations of his results, from which we selectthe foUowiug:— (1) Elliptic cylinder.—The plain and dotted curvilinear arcs contour ,. ,, , , ,. \(?ii ,• lines of nor- are contour lines (coupes topoqraphiques) oi tne section as mai section \ X- r ^ r :i of elliptic cvUnder, as warped by torsion: equilateral wai-ped by torsion; that is to say, lines in which it is cut bya series of parallel planes, each perpendicular to the axis, orlines for Avhich 7 (§ 706) has different constant values. Theselines are [§ 707 (28)] equilateral hyperbolas in this case. The 25-t ABSTRACT DYNAMICS. [708. Contourlin<8 of nor-mal sectionof triangu-lar priHiii, aswarpjd bytorbion. Dincrram ofSt Venantscurvilinearsquares forwliicb tor-sion prob-lem isbolvuljlti. arrows indicate the direction of rotation in the part of theprism above the plane of the diagram. (2) E<iuilateral triangularprism. — The contour linesare shown as in case (1);the dotted curves being thosewhere the warped sectionfalls below the plane of thediagram, the direction ofrotation of the part of theprism above the plane be-ing indicated by the beatarrow. (3) This liagram shows the series of lines represented by(34) of § 70/, with the indicated values for a. It is remarkable
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Keywords: ., bookcentury1900, bookdecade1910, booksubjecttides, bookyear1912
