Art. III. — On the Best Form for a Balance-Beam. 

 By W. C. Kernot, M.A. 



[Read May 13th, 1880.] 



The desirable properties of a balance for accurate weighing 

 will be found set forth in most physical text-books; and for 

 the purposes of this paper reference may be made to 

 Thomson and Tait's Natural Philosophy, Articles 430, 431, 

 and 572 ; and Deschanel's Natural Philosophy (Everett's 

 translation), chapter vii. From these sources the following 

 quotations are taken : — 



"The balance-beam should be as stiff as possible, and yet 

 not very heavy." — Thomson and Tait, Article 430. 



" Thus the stability is greater for a given load — (1) the less 

 the length of the beam; (2) the less its mass; (3) the less 

 its radius of gyration; (4) the further the fulcrum from the 

 beam, and from its centre of gravity. With the exception 

 of the second, these adjustments are the very opposite of 

 those required for sensibility. Hence all we can do is to 

 effect a judicious compromise ; but the less the mass of the 

 beam, the better will the balance be in both respects." 

 — Thomson and Tait, Article 572. 



"The problem of the balance, then, consists in constructing 

 a beam of the greatest possible length and lightness, which 

 should be capable of supporting the action of given forces 

 without bending." — Deschanel, page 82. 



The question, then, is to devise a form of beam which, 

 with sufficient strength and rigidity, shall combine a 

 mininum mass — a problem similar to that with which the 

 engineer has to deal, on a larger scale, in designing bridges, 

 roofs, and other framed structures — the principal difference 

 being that while the majority of our roof and bridge frames 

 are supported at the ends, and loaded at intermediate points, 

 the balance-beam is supported at the centre, and loaded at 

 the ends. 



A fundamental fact that lies at the basis of all economical 

 design is that the longitudinal strength of comparatively 

 long and narrow pieces of ordinary materials is very large 

 indeed, compared to the transverse strength. A wooden 

 lath or rod that would endure a longitudinal compression of 

 hundredweights will break with a transverse force of a few 



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