Van Nostrand's eclectic engineering magazine . ression that the former publicationwas an abstract only, and was possibly too brieffor so valuable an article. A comparison of thetwo, however, shows that our first was so com-plete as to have rendered the second publicationunnecessary in our columns. The discovery wasmade too late to effect a change. VAN NOSTRANDS ECLECTIC ENGIMERmG MAGAZmE. No. , X. THEORY OF AEOHES. {Continued from page 200.) Case VII.—If we construct a curve fromtlie last one by using the same ordinatesand by changing all the abscissas in theratio c: 1, s
Van Nostrand's eclectic engineering magazine . ression that the former publicationwas an abstract only, and was possibly too brieffor so valuable an article. A comparison of thetwo, however, shows that our first was so com-plete as to have rendered the second publicationunnecessary in our columns. The discovery wasmade too late to effect a change. VAN NOSTRANDS ECLECTIC ENGIMERmG MAGAZmE. No. , X. THEORY OF AEOHES. {Continued from page 200.) Case VII.—If we construct a curve fromtlie last one by using the same ordinatesand by changing all the abscissas in theratio c: 1, so that the new co-ordinates of apoint shall he y and c x, and at the sametime change the horizontal forces in thesame proportion, leaving the vertical ones Fig. unchanged; the new curve and new systemof forces so obtained will evidently be par-allel projections of the former, and will bebalanced. This new curve CAB (Fig. 28)is the Geostatic, and bears a relation tothe Hydrostatic strictly analogous to thatbetween the ellipse and circle. Hence, The total vertical load on A B = V = 1 V = pull along cord at B. i /qk \ Total horizontal load on A B =r H = f ^^^^ >c H = pull along cord at A. J The intensities are For vertical load py =- OB cUBc H Forhorizontalloadpa;=^Y-7-= o a !? (36.) (Y H p^ and py referring to the hydrosta-tic curve.) Vol. X.—No. 4—19 The load at A and B and C being alto-gether normal (it is not so at the otherpoints), let po and g\ be the radii of curvature at Aand B. Then In the hydrostatic .. ~ fo=CpyPo cPo = c* Pa • • (37.) 290 VAN NOSTRANDS ENGINEERING MAGAZINE. So But in the hydrostatic 9i=—^ . (38.) These radii are useful in drawing thegeostatic curve. CasQ VIII.—So far we have discussedthe curves assumed by cords under loadsdistributed according to some simplelaw. But it is possible to discuss the moregeneral problem : Given a load that variesand is distributed in any manner, requiredthe curve which it will cause the cord totake; or
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