## Yet more math in bones: calculating weight

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Yes, more math in Bones!  This one from “The Truth in the Lye”, Season 2 Episode 5.  In this episode, a body was found in a bathtub that had been filled with lye, so the body was in an advanced state of decomposition.  (My apologies if you’re reading this over a meal.  It only gets more descriptive, so you might want to skip this post.)

Here Camille Saroyen is talking to the team at the Jeffersonian about how much the person would have weighed.  (I switched to first names for the dialogue, because I had no idea what Camille’s last name was until I looked it up.  Speaking of looking this up, after trying to transcribe it from the DVD I discovered that the whole thing had been transcribed for me here).

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Camille: What’s our starting weight, Zack?

Zack: Starting weight is 542.13. [lbs]

“Bones”: The tub itself weighs about 200 pounds. Capacity is 34 gallons.

Camille: Which at about 8.3 pounds a gallon comes to 270-275.

Jack: And two-thirds full makes it about 180, putting this guy somewhere in the 160-pound weight class.

[Brennan nods]

[Cam is stirring the tub, where orange is starting to appear]

Camille:The cream always rises. Or in this case, melted body fat. [raises tong, melted body fat drips off] I’ll measure its volume to determine body type.

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My initial thought was to figure out if this was good science or not, assuming that it must be because, hey, these people work at the Jeffersonian.  I couldn’t find the weight of a bathtub to check their very first calculation exactly; however, the estimate I found here suggested that clawfoot tubs were 250-350lbs, and modern tubs weigh less, so that 200lbs might well be in the ballpark.

But I started to worry about all the rounding.  Does the tub weigh 200 lbs exactly, or could that be off by 10 lbs?  Then there’s that whole “about two-thirds full”.  Close, but again I suspect a wide margin of error, especially since they rounded when they said that 34 gallons times 8.3 pounds/gallon was 270-275 (It’s 282.2, which is  10 pounds off in a situation that implies accuracy to more than 10 pounds.)

All in all, I think their final answer of 160 lbs (from 542.13-200-180, which equals 162.13) is really pretty rough.  Ballpark, maybe, but it could reasonably be anywhere from 140 to 180 lbs or more.  I want to believe in their good mathematics, but I fear that Barry Leiba was right when he implied in his comment earlier that they’re not really trying to show good science.*

*Not that that will stop me from continuing to talk about it.