Transactions . can be found, givingthe volume of the bead as afraction of the imaginary com-pleted figure. In Fig. 4, ab = B; cd = D;ko 4- oe = II, and amb is the inent cut off. Assuming the completed figure to be asphere, ko = om = co = od = oa = R, or radius of the sphere; and from inspection of the diagram it is clear that - = sin. S cd (S being the angle aoe); and that ko + oe = II = I\ + R cos. 8. The volume of the segment of a sphere, divided by the volume of the sphere, is 3 - — 2 2 Calling this fraction P, the volume of the bead achdb can be ex-pressed as (1 — P) vol. o
Transactions . can be found, givingthe volume of the bead as afraction of the imaginary com-pleted figure. In Fig. 4, ab = B; cd = D;ko 4- oe = II, and amb is the inent cut off. Assuming the completed figure to be asphere, ko = om = co = od = oa = R, or radius of the sphere; and from inspection of the diagram it is clear that - = sin. S cd (S being the angle aoe); and that ko + oe = II = I\ + R cos. 8. The volume of the segment of a sphere, divided by the volume of the sphere, is 3 - — 2 2 Calling this fraction P, the volume of the bead achdb can be ex-pressed as (1 — P) vol. of sphere, on the assumption that thecompleted figure is a sphere. But this would never be th<theoretically, and seldom practically (, within the limits ofpracticable accuracy for the calculation here under considera-tion), for the obvious reason that the effect of gravity, and pos-sibly of other forces, upon the liquid bead must distort it froma perfectly spherical shape. In other words, km in Fig. 4. Diagram Illustrating Calculation ofWeight of Bead from Measurements. 802 DETECTION AND ESTIMATION OF <iOLD AND SILVER, could seldom be safely assumed as equal to cd. Another factormust therefore be introduced to correct the error due to thislack of sphericity. In Fig. 4, ; °d tt 2 TT km = ][ = - II. ke 1 + eos. S Denoting by Q the coefficient of II in this expression, wehave, as the final expression for the volume of the bead, (1 _ P) Q * D2 II. The measurements being in millimeters, it is only necessary tomultiply this volume by the specific gravity in order to obtainthe weight of the bead. A number of beads weighed on a good balance same beads calculated by the above formula mgs. One bead of silver weighing 92 mgs. mgs. Sin. S will not vary much if care be taken not totouch the bead with the tip of the flame after it sets. In goldbuttons the usual effect is to increase H and diminish D, thusgiving too small a value, if on
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Keywords: ., bo, bookcentury1800, bookdecade1870, booksubjectmineralindustries
