Aids to the mathematics of hygiene / [Robert Bruce Ferguson].

  • Ferguson, R. Bruce (Robert Bruce)
Date:
1904
Catalogue details

Licence: In copyright

Credit: Aids to the mathematics of hygiene / [Robert Bruce Ferguson]. Source: Wellcome Collection.

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    i _ ”0 + pt)( 1 - at) ft(l + /3/)( i - «/) (i +«/)(i - n/) — I - (at y- The fraction («/)2 may be neglected, and we have : // = «( i +/3/)(i - «/) = « - nat + nPt—naPt2 = « - nt{a—p) [neglecting («a/3/2)]. Now, a = 000018018, and /3 = o-ooooi878 ; (a—p)— 0-0001614, and the formula A = n—nt(a -p) becomes /i = «-o'oooi6i4«/ ; that is to say, if n = number of divisions read off on the scale, whilst the thermometer stands at t° C., the reading must be diminished by o-oooi6i4«/. For the Fahrenheit scale: The formula will be the same, but with [t-yi) sub- stituted for / ; thus : h=n- n{t- 2,2){a-p). Of course (a — /8) will have a different value. We have seen that «=o-oooiooi. We have also seen that for each degree Centigrade, P=o‘ooooi8y8, and the coefficient of expansion for each degree Fahrenheit is ^ of the coefficient for each degree Centigrade. Therefore, coefficient of expan- sion of brass for Fahrenheit will be : ^xo'ooooi878=o‘ooooio43=/3 ; therefore («— /3)=o,oooiooi -0-00001043 = 0-00008967, and the formula Ji—n — n(l— 32)(a-p) becomes h=n - o'oooo8g6yn(t—32).