In this post, I wrote about the dependence of the volumes of snail shells on their linear dimensions. The theoretical relationship between the shell volumes (V) and a linear shell dimension (L) is given by the power law in the form, V=cL3, where c is a constant.
Tonight, I ask a slightly different question. How does the weight of a snail's shell depend on the linear dimensions of its shell? The answer is easy to derive. Since density is weight divided by volume, the relationship between weight (W) and a linear dimension is also a power law in the form, W=kL3, where k is another constant.
While reading an old paper* today, I came upon suitable data to test the validity of this theoretical relationship. Here are the shell weights of the predatory marine gastropod Urosalpinx cinerea, Atlantic oyster drill, plotted against shell lengths.
The best fit curve is W=5.3x10-5L3.16. Is it close enough to the theoretical relationship?
*J. H. FRASER. 1931. ON THE SIZE OF UROSALPINX CINEREA (SAY) WITH SOME OBSERVATIONS ON WEIGHT-LENGTH RELATIONSHIP. Proc. Malacol. Soc. 19:243-254.