In December 1952, the American Journal of Physical Anthropology published an article with the bureaucratic title “Estimation of stature from long bones of American Whites and Negroes” — an estimate of height from long bones. Its authors were anatomist Mildred Trotter and mathematician Goldine Gleser, both from Washington University in St. Louis. Inside were tables of regression coefficients: measure the length of a skeleton’s femur, tibia, or fibula, plug the number into a formula, and you get the person’s height in life, with an error margin of plus or minus three to four centimeters.
More than seventy years have passed, and those tables are still on active duty: they are used by the DPAA — the Pentagon agency that excavates battlefields from World War II and the Korean War and identifies the remains of the missing. One row in that table — the row for the tibia — turned out to have a biography of its own: a bug that dragged on for half a century, exposed in 2018 in the bones of sailors from the battleship Oklahoma. A story about how a formula built from morgue records outlived its authors — and how strangers fixed it decades later.
A Habr post about a web calculator for estimating the height of ancient hominins from their bones flickered through my feed: enter the length of Lucy’s femur and get 105 centimeters. A fun little toy, but what caught me wasn’t the interface. It was the fine print: under the hood, it runs on tables from 1952 and 1958 — the Trotter tables. I got curious about what “height from bone” even means, and why software from the 2020s is still running on formulas written before transistors.
I’ll be honest: I did not get hold of the primary sources in full — both key articles are behind Wiley’s paywall. But a respectable body of material has formed around them: Trotter’s own 1949 military report, published in full in the WashU medical library archive; the abstract of the 2018 analysis of the tibia bug; biographies of both authors; and teaching tables with the coefficients. That was enough for the following story.
Mildred Trotter did not end up in applied anthropology through some juicy grant. She got there through a dead end. Born in Pennsylvania in 1899, anatomy, a PhD by 1924, a year at Oxford under Arthur Thomson — and her first analysis of Egyptian mummies back in the mid-twenties. By 1948, she had been teaching anatomy in St. Louis for nearly a quarter-century when she took a fourteen-month leave and went to Oahu — to the U.S. Army’s Central Identification Laboratory at Schofield Barracks.
The context is worth taking in. In World War II, the United States lost some 350,000 people; by the time she arrived, the question was how to repatriate around 300,000 remains — and identify them, often from bones, from mass graves, from Pacific islands where bodies had lain for years. The laboratory was worked to the bone: more than 94 percent of the remains that came through received names; when she arrived, the staff included twenty-three embalmers, and the facilities had to be expanded by another 9,000 square feet. But there were no scientific methods: height, age, sex from the skeleton — it was all done by eye and personal experience. In her own 1949 report, Trotter states the principle that would later become the whole field’s charter: “remains are either positively identified or they are not identified — there is no such thing as a preliminary identification.”
Out of that dead end came the motive that matters to us: she simply did not have enough data to predict height from bones. There was no database in which a skeleton’s height in life was reliably documented. In the spring of 1949, she was separately called to Pearl Harbor to examine the commingled remains from the Arizona; she concluded that separating them into individual bodies was impossible, and everyone recovered from the battleship was buried in a common grave at Punchbowl. Remember that place — we’ll return to it in 2018.
Trotter built her database from two sources, and the second was the bleakest.
From 1899 to 1941, Robert J. Terry managed to teach anatomy and collect in St. Louis. Under Missouri law at the time, unclaimed bodies from the state’s hospitals and morgues were transferred to medical schools — the treasury did not want to pay for other people’s funerals. Over forty years, Terry assembled 1,728 complete skeletons from that stream, with unprecedented documentation: name, sex, age, race, cause of death, dates, dental charts, bone inventory. Today it is the Terry Collection, a centerpiece of the Smithsonian’s National Museum of Natural History. The good news: skeletons with documented biographies. The bad news: they are the skeletons of the poor — people who had neither relatives nor money. Any formula derived from such a sample silently carries that bias within it.
And the first source was exactly what Trotter had gone to Oahu for: the remains of military personnel whose height in life had been recorded in enlistment and service files. Dead people with known living height — that is the currency of this science. By combining the morgue and the army, she got what no one else had: a sample in which bone and human height were reliably joined.
Technically, it is modest: linear regression, separate for each bone and group. Here are a few rows from the 1952 tables (bones in millimeters, output height in millimeters; group names use the terminology of the era):
| Group | Bone | Formula | Std. error | N |
|---|---|---|---|---|
| White men | femur | stature = 2.38·F + 614.1 | ±32.7 mm | 714 |
| White men | fibula | stature = 2.68·P + 717.8 | ±32.9 mm | 580 |
| Black men | femur | stature = 2.11·F + 703.5 | ±39.4 mm | 80 |
| White women | femur | stature = 2.47·F + 541.0 | ±37.2 mm | 63 |
Read a row like this: every millimeter of femur adds 2.38 millimeters of height. The coefficients for the same bone differ across groups not because anyone is “different,” but because of proportions: given the same femur length, the trunk and the other segments of the legs supply the remaining height, and their share varies. That is why there is no single formula, and why the table has group coefficients; forget the group, and you will miss by more than the statistical error.
And look at the N column. The white male sample is 714; the female one, 63. The size of datasets is always a cast of who died in wars and whose bodies ended up in documented morgues. The formula faithfully reproduces the structure of its era’s mourning.
Let’s test it on a live example. A femur 452 millimeters long: 2.38 · 452 + 614.1 ≈ 1690 millimeters, or 169 centimeters. Couldn’t be simpler.
Goldine Gleser is a separate story in this pair, one that usually gets lost. She was a mathematician from St. Louis, Phi Beta Kappa at 20, a master’s degree — and then a ninety-degree turn: she left mathematics graduate school after getting married, returned to scholarship through psychology, and did not earn her doctorate until 1950. She calculated Trotter’s regressions as a mathematician for mathematicians.
After that, her career moved into entirely different worlds: with Cronbach, she wrote Psychological Tests and Personnel Decisions (1957), a classic of decision theory about people, and helped develop generalizability theory — the very apparatus used today to assess how reliable any measuring instrument is. She worked on the traumatic aftermath of the Buffalo Creek flood, became a fellow of the American Statistical Association, and physical anthropology was, in essence, a side line for her. But every copy of the Trotter-Gleser tables bears both names — and for half a century, the male side of the profession cited a woman mathematician who did not derive the formulas but calculated them.
Six years later, Trotter and Gleser published a revision — with the admirably honest title “A re-evaluation of estimation of stature based on measurements of stature taken during life and of long bones after death.” Its substance lay in three things. First: the matching itself was reconsidered — height in life is measured by one set of rules, bones after death by another, and there is a systematic difference between them that has to be carefully folded into the formula. Second: the sample was supplemented with data from those killed in the Korean War — skeletal materials were processed at the American identification laboratory in Kokura, Japan, and by 1958 there were separate equations for Asian groups (still used to this day, which Korean anthropologists addressed in a separate warning in 2016).
The third thing was the very thing from which the bug would grow half a century later: the tibia data acquired a correction on the order of ten millimeters. How exactly it was formulated and applied, I could not reconstruct from the sources available to me — that was formally what the later dispute was about. For now, let us simply note this: in the 1958 edition, the tibia row lives with a tiny but consequential footnote.
Kokura deserves a word of its own, because it is an almost forgotten knot of the war now. The American Central Identification Unit worked in this Japanese city from 1951 to 1955, processing remains from the entire Korean War. In September–October 1954, after the armistice, Operation Glory took place — an exchange of remains: North Korea and China handed over around four thousand bodies of UN soldiers; around fourteen thousand went in the other direction. Of the transferred remains, about 1,900 were American, and some 850 of those remained unidentified — buried as unknowns at the National Memorial Cemetery of the Pacific in Punchbowl Crater, Hawaii. From this knot of heat, mass graves, and commingled bones came the data on which the second Trotter-Gleser edition became a world standard.
As always in the science of war: the more terrible the material, the longer it goes on working afterward.
Now for the Oklahoma guinea pig. The battleship sank at Pearl Harbor on December 7, 1941; the remains of her crew lay at Punchbowl for decades as unknowns — in the same national memorial cemetery in the crater where the unidentified from the Arizona were buried. In the 2010s, the DPAA began a full exhumation and analysis of these commingled bones using a new generation of software — Fordisc, the standard forensic program into which the historical data of Trotter and Gleser had been embedded as a reference corpus.
And then something awkward surfaced. In 2018, a team led by Lynch, Brown, and co-authors showed in the Journal of Forensic Sciences that for roughly ten years, Fordisc’s estimates of height from the tibia had been systematically low by an average of 1.25 inches — about three centimeters — relative to estimates from other bones on the same skeletons. The cause was trivially nightmarish: in the software implementation, the correction to Trotter’s tibia data had been applied as 20 millimeters instead of the original 10, and the defect sat specifically in the package’s third version. An extra ten millimeters in the correction — and the entire row of the table slid downward by an average of an inch. On top of that, in five percent of predictions, actual height in life fell outside the declared prediction interval — meaning the software, honestly reporting “± so many centimeters,” was lying even in its honesty. And the most piquant part: even after the correction was restored to the original 10 millimeters, tibia estimates remained slightly low — which means the question of the 1958 sample measurements runs deeper than a single typo.
This was not, by the way, the first expedition against that row. Back in 1994, Jantz, Hunt, and Meadows published a paper with a title fit for a detective thriller: “Maximum length of the tibia: how did Trotter measure it?” Forty years later, people were literally reconstructing from indirect evidence exactly what anatomical method Trotter had used when she put calipers to a shinbone. A year later came the sequel — “The Measure and Mismeasure of the Tibia.” And in 2006, anthropologist Klepinger put forward a position I would hang in every handbook: uncertainty in measuring a bone can kill its usefulness, even if its regressions formally have a lower standard error than the neighboring ones.
Today, the DPAA works with “corrected historical Trotter data,” and most of this machine’s little wheels have been screwed back into normal working order. But the precedent itself is worth more than one row in a table.
Other families of methods were built in parallel, and they are worth listing so it does not seem as though the regressions of 1952 were the only option.
The anatomical method of Fully (1956) works in reverse: it adds up the heights of all the bones in the skeleton from crown to heel, then adds a correction for soft tissue. It is more accurate than regressions, but it requires an intact skeleton — a luxury unavailable on a battlefield or in a commingled grave; no wonder military forensics chose short formulas. A version without the skull and vertebrae was proposed by Fully and Pineau in 1960, and a full modern revision of the approach was done by Raxter and co-authors in 2006.
An alternative of another kind is unified one-shot constants. Feldesman and colleagues ran 13,149 people from 51 populations through the numbers in 1990 and got an almost culturally invariant rule: femur length is roughly 26.7 percent of height, therefore height = femur length · 3.7456. No group coefficients, no ethnography — one bone, one multiplier. In the Habr example, the two approaches converge: a 452 mm femur gives 169 centimeters both under Trotter-Gleser for white men and under Feldesman.
And, of course, paleoanthropology. Lucy, AL 288-1, comes out at 105 centimeters under those same constants; according to modern summaries, her body mass was around 26 kilograms, with a range from 17 to 39. Formulas written using soldiers from the 1950s roll quite comfortably onto an australopithecine from three million years ago. There’s your legacy code.
The first lesson is about measurement conventions. The Trotter-Gleser formula is not merely a coefficient and an intercept; it is a convention embedded inside the formula for exactly how to measure the bone. Fordisc treated historical data as though it were self-evident, applied a correction twice as large as it should have been — and for half a century did not notice that it had broken its contract with a dead author. Documentation of the measurement procedure is not an appendix to the result. It is part of the result itself. Any dataset that does not say “which end they measured from” is a weight hanging over a timer.
The second lesson is about provenance. The Terry Collection and military service records are data with an author, a date, and honestly described distortions. That is precisely why they could be supplemented and reconsidered in 1958, 1994, and 2018 — and why the bug eventually surfaced, because every number had a lineage. A database without provenance is not a database. It is an anecdote.
The third is about people. Gleser came to the table as a mathematician on an accidental assignment and left to build psychological measurement; Trotter stayed in anatomy, became the first woman president of the American Association of Physical Anthropologists (1955–1957), received the Viking Fund Medal, and at 86 survived a stroke and bequeathed her body to that same medical school in St. Louis — closing the circuit herself, from the inside. In the collection I used to write this text, her own named entry is there too.