Chapman’s death.

[JeffHamm]

This is from Shivpoojan K. (2018). Time since Death from Rigor Mortis: Forensic Prospective. J Forensic Sci & Criminal Inves 2018; 9(5): 555771. DOI: 10.19080/JFSCI.2018.09.555771.

...

Anyway, there's also Table 1 on page 3, that lists the number of cases where rigor was complete, after various hours (2 were complete by 2 hours)

Number of cases postmortem at which rigor was complete (hrs)
	Cases	Hours
	2	2
	14	3
	31	4
	14	5
	20	6
	11	7
	7	8
	4	9
	7	10
	1	11
	1	12
	2	13

So as we can see, while rigor is, on average, complete around 5.7 hours, the variation is quite large and to apply that average to a specific case without considering the margin of error, would be unwise. The standard deviation (average amount by which an individual case differs from the mean) is over 2 hours for this data (2.36), Which means, 95% of cases will have reached full rigor between 1 and 10 hours after death. (well, not quite as the data isn't normally distributed, but even accounting for the skew we're talking 95% show full rigor between 3 and 12 hours. So if Dr. Phillips recorded the time when full rigor was reached, the ToD would be estimated to be between 3 and 12 hours earlier, which I rather suspect will include the witnesses time window.

- Jeff

https://juniperpublishers.com/jfsci/....ID.555771.pdf

Ok, just geeking out here. I posted this a while back (a table on times until full rigor mortis from a research article I came across). Anyway, as the table shows, individual cases vary in the time to reach full (not onset time, but full rigor) from 2 to 13 hours. I've been analysing the data a bit as I've been working on some routines to fit distributions of data (to find the equation that describes them). Basically, using this data as my example, we plot hours on the x-axis and then the percentage of all the data that would have reached full rigor by this point in time. So, for 4 hours, we just add up the number of cases for 2, 3, and 4 hours, and plot that percentage of the 114 cases. This is just a cumulative total plot. Then, you find the equation that describes that relationship between hours and probability of reaching full rigor at or before that time, and there you have it.

The data for rigor follows what's called a "log normal distribution". Basically, if you take the natural log of the hours, then look at the distribution it will be normal (typical bell shaped distribution). Log normal distributions are skewed in terms of the "hours", but are normally distributed in terms of the "ln(hours)".

I've plotted the data and the model function:


if you want to play with it, and have excel, if you paste the following into Cell B1, then you can enter a number of hours in Cell A1 and the formula will return the probability of reaching full rigor by that time.

=NORMSDIST((LN(A1-0.648)-1.38)/0.527)

Also, the 95% confidence interval is that a body will reach full rigor between 2.05 and 11.8 hours, with half reaching full rigor after 4.625 hours.

now, I don't know under what conditions this data was collected (it's certainly not going to be ones similar to how Annie Chapman was found, but far more likely going to be people who died in care, so at room temperatures, not disemboweled, etc. Be that as it may, I thought some may be interested.

- Jeff

[JeffHamm]

Ok, I can't resist playing with this.

Dr. Phillips testifies that he arrived at the scene at 6:30, and performed his examination at the "mortuary" shortly after 2. So that's a bit more than 7 hours 30 minutes after he arrived, but as I don't know what "shortly after" is in terms of minutes, we'll just call it 7 hours 30 minutes. At 2 he notes the stiffness of the limbs is "well marked", so if that is full rigor then not entirely surprising. Even if Dr. Phillips killed Chapman at 6:30, by 7 hours and 30 minutes later 85% of cases would be in full rigor (let's pretend the above data is at all useful with regards to Annie Chapman's case, which, to be honest, I know it's not, but I'm playing here )

Now, if 2 o'clock is full rigor, from the above data we have our 95% confidence interval. That means, her ToD would have to fall between 2.05 hours earlier than 2, (so shortly before noon ) and extending back in time as far as 11.8 hours, which would be 2:12 am. Basically, we know she was dead around 6, so based upon the reported time of full rigor, we can narrow down her ToD to anywhere after 2:12 am up until she was found, with 95% certainty. Given we know she was eating potatos around 1:30, which is when she left to get money. We've reduced our time window by almost 45 minutes!

And of course, since it's possible she was in full rigor before Dr. Phillips checked, if that happened an hour earlier, our "window of consideration for ToD" will span times both when she was known to be alive (it will extend past the time she was eating potatoes by about 15 minutes), and known to be dead (because the 95% time window will end around 11, 5 hours after she was found dead). What I'm getting at is that the margin of error for this kind of data is so wide that it doesn't help us, because the evidence we have from the witnesses narrow the time window even more than this can.

- Jeff

[Trevor Marriott]

Ok, I can't resist playing with this.

Dr. Phillips testifies that he arrived at the scene at 6:30, and performed his examination at the "mortuary" shortly after 2. So that's a bit more than 7 hours 30 minutes after he arrived, but as I don't know what "shortly after" is in terms of minutes, we'll just call it 7 hours 30 minutes. At 2 he notes the stiffness of the limbs is "well marked", so if that is full rigor then not entirely surprising. Even if Dr. Phillips killed Chapman at 6:30, by 7 hours and 30 minutes later 85% of cases would be in full rigor (let's pretend the above data is at all useful with regards to Annie Chapman's case, which, to be honest, I know it's not, but I'm playing here )

Now, if 2 o'clock is full rigor, from the above data we have our 95% confidence interval. That means, her ToD would have to fall between 2.05 hours earlier than 2, (so shortly before noon ) and extending back in time as far as 11.8 hours, which would be 2:12 am. Basically, we know she was dead around 6, so based upon the reported time of full rigor, we can narrow down her ToD to anywhere after 2:12 am up until she was found, with 95% certainty. Given we know she was eating potatos around 1:30, which is when she left to get money. We've reduced our time window by almost 45 minutes!

And of course, since it's possible she was in full rigor before Dr. Phillips checked, if that happened an hour earlier, our "window of consideration for ToD" will span times both when she was known to be alive (it will extend past the time she was eating potatoes by about 15 minutes), and known to be dead (because the 95% time window will end around 11, 5 hours after she was found dead). What I'm getting at is that the margin of error for this kind of data is so wide that it doesn't help us, because the evidence we have from the witnesses narrow the time window even more than this can.

- Jeff

My advice is stop playing, ask your ward manager to let you out more !

Dr Phillips at crime scene "Stiffness of the limbs was not marked, but it was commencing"

www.trevormarriott.co.uk

[JeffHamm]

Ok, last bit based upon this. Now, what having that equation allows us to do is calculate the percentage of cases that reach full rigor between time A and B. So, things like "how many cases reach full rigor between 1 and 1.5 hours after death?". This is called the "density function" while the above one is the "cumulative function". Basically, they contain the same information just presented in a different way (you can think of the density function as the individual numbers and the cumulative as their running total, so the change in height between two points on the cumulative plot is what is shown in the density plot).

I've divided the 0-13 hours into 30 minute blocks, to show the density plot below. Basically, it shows the most common time would be around 4-4.5 hours after death, but even the most common time is only just above 10%. But, what this would let you do is make a call based upon probabilities. If you knew when someone died, and were told they reached full rigor either 2-2.5 hours later or it was 6-6.5 hours later and you had to bet on which one it was, you would see that the 6-6.5 density is higher than the 2-2.5, so the 2nd would be the more probable. So even though neither of those time slots is very probable to begin with, since you only have two to choose from, it's the relative probabilities that matter.


Now, we can just flip this density plot around, and use it to do exactly the same thing but the other way; if we know what time someone reached full rigor, we can compare the relative probabilities as to when the ToD was. We don't actually know the time Chapman reached full rigor, but we do know that at 2 she is reported to be in what appears to be full rigor. So I've locked to that time for now. And, I've marked the time of her last known sighting (around 1:30) and when she was found (around 6 am) with two dashed black lines. Her ToD has to be in there somewhere. I've also marked Dr. Phillips estimated time (4:30 ish) and the witness based time (5:30ish) with coloured lines.



Even if we keep sliding things "to the left", meaning we presume she reached fill rigor by larger amounts before Dr. Phillips examined her at 2, you can see what will happen. For the vast majority of those times, the witness estimate for the ToD will have the greater of the two probabilities. She would have had to reach full rigor by 8:30 before that changes and the witnesses time starts becoming the less likely, and only 37% of cases reach full rigor in 4 hours (and people are arguing that with Chapman rigor should be slowed due to cold, etc). And if we set the time she reached full rigor at the time the cumulative plot tells us 50% of cases do (so we're at a coin flip), then that is later, making the witness time the more probable. Unfortunately, we don't actually know when she reached full rigor, so we can only make probabilistic statements, and given what we do know, based upon the rigor data we do have, the witness time is the more probable. More importantly, all of this data is going to based upon cases very very different from Chapman's situation, so I'm certainly not presenting this as definitive of anything really. What I am trying to demonstrate, though, is how one might use this kind of data to make more objective decisions, and also to show just how wide the error is associated with this. It's better than chance, but it's still not the kind of precision that people seem to think it is.

- Jeff

[JeffHamm]

My advice is stop playing, ask your ward manager to let you out more !

Dr Phillips at crime scene "Stiffness of the limbs was not marked, but it was commencing"

www.trevormarriott.co.uk

Which means she wasn't in full rigor. The data I'm working with isn't about the onset time but when full rigor is reached. Clearly, Dr. Phillips is telling us she hadn't reached full rigor. Rigor is a result of chemical processes in the body that begin pretty much when someone dies, so technically rigor begins at the point of death, it just isn't detectable by moving the body until sometime later. Cold slows down those chemical reacations, so it builds up more slowly, but the process is still going on. The chemical processes stop, however, somewhere around 5C I believe, so in those situations rigor doesn't start until the body warms up and the reactions start.

So the fact that he could detect that it was starting doesn't tell us the rate at which it was progressing, or for how long it was going on. It may have been going on for an hour, or for two, etc.

Anyway, I'm taking your good advice and am off to quizz night. But seriously Trevor, I'm not presenting this as definitive by any stretch, but it is all we have and before people start throwing around arguments about what things like "rigor was detected" etc means in terms of it's predictive ability, it is important to look at the data. This is one set I found so I'm using it to demonstrate the issue. Based upon this data, the witness time window would be the objectively more likely - but it's not conclusive. Sometimes the less likely thing happens, but probabilities are all that we have to work with. Hence, this is why I keep talking about "the most likely ToD" rather than the "proven ToD". It's just the one that is more probable.

- Jeff

[Trevor Marriott]

Which means she wasn't in full rigor. The data I'm working with isn't about the onset time but when full rigor is reached. Clearly, Dr. Phillips is telling us she hadn't reached full rigor. Rigor is a result of chemical processes in the body that begin pretty much when someone dies, so technically rigor begins at the point of death, it just isn't detectable by moving the body until sometime later. Cold slows down those chemical reacations, so it builds up more slowly, but the process is still going on. The chemical processes stop, however, somewhere around 5C I believe, so in those situations rigor doesn't start until the body warms up and the reactions start.

So the fact that he could detect that it was starting doesn't tell us the rate at which it was progressing, or for how long it was going on. It may have been going on for an hour, or for two, etc.

Anyway, I'm taking your good advice and am off to quizz night. But seriously Trevor, I'm not presenting this as definitive by any stretch, but it is all we have and before people start throwing around arguments about what things like "rigor was detected" etc means in terms of it's predictive ability, it is important to look at the data. This is one set I found so I'm using it to demonstrate the issue. Based upon this data, the witness time window would be the objectively more likely - but it's not conclusive. Sometimes the less likely thing happens, but probabilities are all that we have to work with. Hence, this is why I keep talking about "the most likely ToD" rather than the "proven ToD". It's just the one that is more probable.

- Jeff

Hi Jeff
I am just kidding and I know you mean well, but the reality is we are never going to know, even with those who say that based on the witness testimony it could be after 5am, as keeps getting said both Phillips and the witness testimony are "unsafe" to totally rely on to prove a conclusive TOD, what else can be said?

https://www.trevormarriott.co.uk

[FISHY1118]

Sorry...we are arguing about an earlier TOD than indicated by Phillips when compared with the witness statements? If Long and Cadosche happen to both be correct, then Annie is still alive, right? If just one is correct, then Annie is alive at that time, right? If you accept ALL the relevant witnesses, Richardson, the Cadosche, then Long, then Davis, then Annie alive until around 5:30, correct? Then the summary is that Phillips was wrong, simple, and no need for the petty BS that has ensued here.

This makes no sense at all in regard to my post , gibberish im afraid

[FISHY1118]

what do you mean by 'scenario'? The testimony of richardson, long and cadosch is fact - they did say what they are reported to have said. And i don't think anyone is seriously saying that there testimony proves chapman's time of death. There are problems with their testimony which argues that we adopt caution, but nothing proves their testimony should be disregarded.

oh thats where you be wrong ..... Herlock believes just that . There in lies the problem

[FISHY1118]

HEY HERLOCK, WERE 3 DOCTORS RIGHT IN THEIR TIME OF DEATH WITH EDDOWES STRIDE AND NICHOLS ? ..... ANSWER ''YES'' SEE NOT SO HARD IS IT. COULD HAVE SAVED YOU A LOT OF TIME WITH THAR DRIVEL THAT YOU JUST TYPED

[PaulB]

Hi Jeff
I am just kidding and I know you mean well, but the reality is we are never going to know, even with those who say that based on the witness testimony it could be after 5am, as keeps getting said both Phillips and the witness testimony are "unsafe" to totally rely on to prove a conclusive TOD, what else can be said?

www.trevormarriott.co.uk

So what do you propose doing with Phillips' and the witness's testimony? You repeatedly assert that you are not dismissing it, so what are you doing with it?

[PaulB]

oh thats where you be wrong ..... Herlock believes just that . There in lies the problem

I don't think Herlock does believe that the witness testimony proves Chapman's time of death. He has presented a number of authorities who he probably correctly believes demonstrate that Dr Phillips' estimated time of death was highly unreliable at best, and he has pointed to three witnesses whose combined testimony suggests a time of death after 5:15am. He is clearly aware of the problems presented by their testimony because he has acknowledged those problems and discussed them, and, as said, whilst the problems argue that we adopt caution, nothing proves their testimony wrong or that it should be disregarded.

[Trevor Marriott]

So what do you propose doing with Phillips' and the witness's testimony? You repeatedly assert that you are not dismissing it, so what are you doing with it?

Treating it all alike as unsafe to totally rely on to be able to conclusively prove a time of death beyond a reasonable doubt.

https://www.trevormarriott.co.uk

[FISHY1118]

I don't think Herlock does believe that the witness testimony proves Chapman's time of death. He has presented a number of authorities who he probably correctly believes demonstrate that Dr Phillips' estimated time of death was highly unreliable at best, and he has pointed to three witnesses whose combined testimony suggests a time of death after 5:15am. He is clearly aware of the problems presented by their testimony because he has acknowledged those problems and discussed them, and, as said, whilst the problems argue that we adopt caution, nothing proves their testimony wrong or that it should be disregarded.

''He has presented a number of authorities who he probably correctly believes demonstrate that Dr Phillips' estimated time of death was highly unreliable at best,''

SO WHY CANT HE SAY THE SAME WORDS WHERE LONG CODOSCH AND RICHARDSON ARE CONCERNED AS BEING UNRELIABLE AND CONTRADICTORY? AND THAT CHAPMAN ''COULD'' INDEED HAVE BEEN KILLER EARLIER THAN 5.30 ?

IF HE DID ID GLADLY NOT POST ANOTHER THING ABOUT CHAPMAN ..... HMMMM BUT HE WONT

[Herlock Sholmes]

HEY HERLOCK, WERE 3 DOCTORS RIGHT IN THEIR TIME OF DEATH WITH EDDOWES STRIDE AND NICHOLS ? ..... ANSWER ''YES'' SEE NOT SO HARD IS IT. COULD HAVE SAVED YOU A LOT OF TIME WITH THAR DRIVEL THAT YOU JUST TYPED

It’s pointless talking to you Fishy because you simply ignore other posts unless they come from Fisherman.

Ive explained this point to you two or three times. Even a very small child could understand it but you seem unable to. It’s more likely of course that you do understand it but you simply lack the honesty and integrity to concede the point.

This is what you need to do Fishy....contact a few authorities on Forensic medicine and say this:

Hello, my name is Mr Fishy. In all of your books and all of the papers that you’ve written you have said that estimating TOD using Rigor and Algor is unsafe and unreliable and should not be used. Because of this some people are saying that Dr Phillips couldn’t have accurately given Annie Chapman’s TOD. You are all wrong I’m afraid and this is why.......three Victorian doctors got a TOD correct....therefore all doctors must have been able to estimate TOD accurately. As I’ve educated you could please change all of your books and acknowledge how brilliant I am and how dumb you all are for missing this.

Yours Faithfully
Mr Fishy.


Try this Fishy and let us know how you get on.

[Herlock Sholmes]

''He has presented a number of authorities who he probably correctly believes demonstrate that Dr Phillips' estimated time of death was highly unreliable at best,''

SO WHY CANT HE SAY THE SAME WORDS WHERE LONG CODOSCH AND RICHARDSON ARE CONCERNED AS BEING UNRELIABLE AND CONTRADICTORY? AND THAT CHAPMAN ''COULD'' INDEED HAVE BEEN KILLER EARLIER THAN 5.30 ?

IF HE DID ID GLADLY NOT POST ANOTHER THING ABOUT CHAPMAN ..... HMMMM BUT HE WONT

Everything that I’ve said about Long, Richardson and Cadosch has been exactly correct. I’ve discussed every single issue (like the contradiction in timing between Long and Cadosch) I’ve never said that anything is 100% certain.

[B]SO WHY CANT HE SAY THE SAME WORDS WHERE LONG CODOSCH AND RICHARDSON ARE CONCERNED AS BEING UNRELIABLE AND CONTRADICTORY? AND THAT CHAPMAN ''COULD'' INDEED HAVE BEEN KILLER EARLIER THAN 5.30 ?

Chapman could have been killed earlier. I’d say that it was around a 1 or 2% chance. If that.

We have two parts Fishy.

Was Phillips TOD estimate unsafe and unreliable?

Yes....absolutely....undoubtedly....categorically. .....without a single, solitary, scintilla of doubt!

Was Cadosch unsafe and unreliable?

No...he was simply cautious on which direction the ‘no’ came from. This points to honesty. The chances of him heading something coming from that yard, at that time, and it not being connected to the murders is tiny.

Was Richardson unsafe and unreliable?

Of course he wasn’t. Chandlers unverified comments from the passageway interview might easily have been a mis-hearing or a mid-remembering. Apart from that there would have been nothing suspicious about him saying that he checked the cellar doors without mentioning sitting on the steps. To read more into it is desperate nitpicking. Under oath at The Inquest he said that he could not have missed a body had it been there. You can’t get much stronger witness evidence than this. He was 100% certain.

Was Long unsafe and unreliable?

Her timing is certainly an issue. She may simply have been mistaken and seen someone else. It’s a possibility but an unlikely one imo. As we know that timings have to be taken with a pinch of salt due to the absence for most of watches and clocks we have at least a plausible explanation (of course Fishy is again the only person in the world that doesn’t accept that times could be inaccurate because of these facts) If we simply postulate that both Cadosch and Long were 7 or 8 minutes out with their timings then it all fits a timeline.

All this makes it overwhelmingly likely that Chapman died around 5.25/5.30. This comes from following logic, Forensic authorities, common sense and the absence of bias. It’s why the sensible, unbiased posters all agree.

This is as close as we will ever get to a definitive answer. We will never be 100% certain unless previously unknown evidence is discovered which causes us to re-evaluate. But this is how we stand.