Johnson Daniel P
Institute for Basic Standards, National Bureau of Standards, Washington, D.C. 20234.
J Res Natl Bur Stand A Phys Chem. 1974 Jan-Feb;78A(1):41-48. doi: 10.6028/jres.078A.005.
Expressions are derived for the volume of an approximate sphere in terms of measured breadth, the distance between parallel planes tangent to opposite sides. The difference in volume of a ball and a true sphere of the same average breadth is shown to be of second order, and much smaller than the random and systematic errors in the measurements of the dimension. Thus, a ball commercially available at moderate cost can be used for absolute density measurements of high accuracy. Similar expressions are given for the area of an approximate circle.
根据测量的宽度（即与相对两侧相切的平行平面之间的距离），推导了近似球体体积的表达式。结果表明，具有相同平均宽度的球和真正球体在体积上的差异为二阶，并且远小于尺寸测量中的随机误差和系统误差。因此，以适中成本可购得的球可用于高精度的绝对密度测量。还给出了近似圆面积的类似表达式。
