full size?

[Kane]

This is not an ID question, but more a morphology one to determine likely size. I can't recall where I once chanced upon a formula for judging what the full size of a trilobite (pending species) would have been on the basis of a fragment. This one would have been a fairly substantially sized bug, but not by any means the biggest. It is a typical Eldredgeops rana. It is likely just a moult, and perhaps there is a (very) slim chance I might be able to find the full one in the vicinity.

Measuring to just at where the halfway point of the glabella is, I get a reading of 1.8 cm (0.71 inches) for a possible total width at the cephalon of approximately 3.6 cm (1.42 inches).

Any experts have the "magic formula" for measuring this species so that I can perform this on some of my other specimens?

Edited August 23, 2016 by Kane

[tmaier]

If the relative geometry remains the same in the growth through to adulthood, then you can use ratiometric calculation...

First set up your ratio. Value of cephalon width of Known specimen over total length of same Known specimen... that becomes our standard ratio. You need to measure some other specimens to verify that this is indeed a stable linear ratio.

So our linear equation is Kc/Kl = Uc/Ul, Known cephalon over Known length is equal to Unknown cephalon over Unknown length.

Then plug and punch... plug in you values and punch out the answer. For example, using just some random values, if the Known specimen is cephalon 0.4 and total length 1.1, then we have 0.4/1.1=1.4/x. Cross multiply and divide, and you get (1.1*1.4)/0.4=3.85 inches.

I would have to say that the answer above is ~4 inches, because in the data above I only had one significant digit for the width of the known cephalon head, so that limits my final precision to only one digit of significance. So if you want to keep the two digits of answer, you need to measure more accurately.

Just as an example....

That only applies to a linear expansion. In some creatures this will not apply.

I'm not sure if that was what you needed?

[Kane]

Thanks, tmaier! That is precisely the equation I needed. As I have a few prone specimens, I'm going to set about measuring those (something I should have thought to have done first, so my bad) to obtain an average, and apply the ratio as per above.

I do suspect just from the initial fragment that this was a fairly big boy for this genus. I'm going back this morning in search of that same stone, cleave it more finely in the dim hopes of finding more moult pieces.

[tmaier]

Pull up images on the internet to verify that the ratio doesn't change, as proof that your method is sound. To make it easy, I would take the images and pull them into a image program like GIMP of Paint, and then do a check on the pixel ratio. A ratio is a ratio, no matter what the units were that gathered the data, so pixels can be used without messing around with units conversions.

So for example, I find a whopper big specimen image on the internet with cephalon width of 320 pixels, and length of 880 pixels. That's a ratio of 320 to 880, or 320/880=0.3636. Then I find a small specimen and find it has the pixel ratio of 0.365. Those two ratios are so close, I can use them as proof that the growth geometry is linear, and then I can proceed on to using those numbers to solve my problem.

You can also mix units in a ratiometric comparison. So lets say my known is in pixels, and my unknown is in inches. No problem!

320pixels/880pixels = 1.4inches/x inches. I cross multiply and divide, and my answer comes out in inches.

And also watch your significant digits. To pull two digits in my answer above, I would have to measure that cephalon to 0.42 inches. Any digits that pop out in the final answer that go beyond the level of significance of the initial data are just noise, so you have to round them out. Notice in the ratio above I had three significant digits for my pixel count, but I use a four digit number to calculate. You carry the ""numerical noise" through the calculation, and only round at the end, so I kept those four digits. There is a wee-bit-o-significance in that fourth digit, and I don't want to throw it away until I'm done.

[Kane]

Thanks again! I spent some time with my own specimens (as well as some online images) measuring. I didn't go right down to the pixels per se as I am looking for an approximate number (so I used the very high tech solution of putting my ruler up against my screen to measure length and width, making that a ratio between L and W). Averaging out all the readings to get to a median, I applied this to the cephalon (effectively doubling the width from the centre of the glabella to the lateral margin to get the cephalon's width). In its full, living state, it would have been a fairly substantial size for this species, at 2.9" +/- 0.05" (~7.42cm) in length. That being said, some have been recorded up to 4" (although I don't think that has been confirmed as they usually max out in the literature to about 3")

The missing part of the cephalon is non-retrievable as the cut-off is also the edge of the stone, long ago eroded. I sliced and diced the remaining rock fragments for more traces, but to no avail. A rather fragmentary and thus disappointing specimen, but an example of this species at the the upper limit in terms of size if my arithmetic is correct.

Edited August 24, 2016 by Kane