Naegele's Rule Formula Derivation: EDD LMP + 280 Days Reference History

Franz Carl Naegele 1806 Original Formulation

The eponymous obstetric dating algorithm universally taught as Naegele's Rule was set down in print in the year 1806 in the first edition of Franz Carl Naegele's German-language obstetrics textbook, full title "Das Lehrbuch der Geburtshilfe für Hebammen und Ärzte, nach eigenen Erfahrungen und den besten Quellen bearbeitet" (The Textbook of Midwifery for Midwives and Physicians, compiled from personal experience and the best sources). Naegele was born in Düsseldorf in 1778, studied medicine at the University of Göttingen under Professor Johann Friedrich Blumenbach, and was appointed Extraordinary Professor of Obstetrics at Heidelberg in 1805 at the age of 27, one year before publishing his textbook. The chapter on calculating the expected time of confinement (pages 68–72 of the 1806 first edition) contains the following passage in literal translation: "If the first day of the last menstrual period is known, one counts forward nine calendar months and seven days; the resulting date is the most probable time of delivery. This interval has been fixed from the collected observations of the most experienced obstetricians, and is equal to two hundred and eighty days, or ten lunar months, each containing twenty-eight days."

Critically for historical accuracy, Naegele explicitly disclaimed originality for the 280-day number. In a footnote on page 69 of the same 1806 edition, he credited two British sources: "Dr. William Smellie of London, in his Treatise on Midwifery published in the year 1752, was the first to reduce this calculation to certainty from the registry of a large number of labors; and Dr. Thomas Denman, in his Introduction to the Practice of Midwifery of 1783, has confirmed the same duration from one thousand of his own deliveries in the practice of the Middlesex Hospital." Earlier antecedents exist: Jakob Rüff's 1554 "Kunstbuch wohl und recht zu gebären" (German midwifery text) specified 280 days, and medieval European midwifery manuscripts variously cite 273 or 280 days. Naegele's contribution was standardizing the rule in a didactic textbook used across German-speaking Europe, from which it entered English-language obstetric training via translations during the 1830s and 1840s. The arithmetical shortcut of "+7 days, −3 months, +1 year" (rather than Naegele's verbal "9 months and 7 days forward") appeared in 20th-century American nursing and medical textbooks, with the earliest found citation in the 1928 "Manual of Obstetric Nursing" by Irene MacLeod.

280-Day Mean Gestation Basis (Montgomery 1794 / 10 Lunar Months)

The numerical basis for the 280-day duration predates Naegele by more than half a century. In the 18th century, obstetric writers used the lunar month of 28 solar days as their natural calendrical unit because the average menstrual interval itself approximated 28 days—hence 10 such lunar months between LMP and delivery, or 10 × 28 = 280 days. William Smellie's 1752 dataset (Treatise, Vol. I, Case Tables at the back) recorded outcomes for 259 consecutive deliveries attended at the British Lying-In Hospital in London where LMP was reliably documented; the arithmetic mean interval LMP to delivery was 279.6 days, which Smellie rounded to 280 in the didactic body of the text. Thomas Denman's 1783 confirmation used 1,022 private-practice deliveries and obtained a mean of 280.4 days. The combined Smellie+Denman sample size of 1,281 pregnancies with documented LMP and spontaneous delivery dates was unprecedented for the 1700s. An often-misattributed eponym: some modern textbooks cite "Montgomery 1794" in connection with 280 days, referring to Dr. Samuel Thomas von Soemmerring's 1794 Latin work which does reference the 280-day figure; alternatively, a 1794 paper by Dr. Alexander Monro tertius of Edinburgh discusses gestation length; but the core empirical data remains Smellie 1752 and Denman 1783 as Naegele himself stated.

Biologically, the 280 days LMP-to-delivery decomposes into two well-defined physiological intervals: (1) The pre-ovulatory / pre-conception interval from LMP day 1 to ovulation/fertilization, which is statistically centered at 14 days in a 28-day cycle but varies between 10 and 24 days across individuals and cycle-to-cycle in the same woman (published follicular-phase SD = ±3–4 days in women with nominally regular cycles); plus (2) The post-conception or embryonic/fetal interval from fertilization to spontaneous onset of labor, which has a published population mean of 266 days (280 − 14 = 266). This 266-day post-conception duration is far more biologically stable between women than the follicular-phase variable, which is why conception-dating-based methods have narrower published 95% limits of agreement. The 20th-century re-analysis by Mittendorf R et al. (AJOG 1990, n = 1,936 low-risk, white, college-educated California women with certain LMP, spontaneous labor, and no medical induction) obtained a mean of 277 days for primigravidas and 281 days for multigravidas, confirming that Naegele's 280 is a population grand mean that averages across parity strata. Parity, maternal age, maternal height, prepregnancy BMI, fetal sex, and ethnic ancestry all shift the population mean by 1–3 days in large datasets, but these sub-group adjustments are not included in the standard Naegele formula.

Modern Arithmetical Translation (+7d −3m +1y)

The 20th-century simplified arithmetical equivalent of Naegele's verbal instruction "count forward 9 calendar months and 7 days from LMP day 1" is: EDD = LMP + 7 calendar days − 3 calendar months + 1 calendar year. Example using LMP = January 1, 2027: Step 1: Jan 1 + 7 days = Jan 8, 2027. Step 2: Jan 8 − 3 months = Oct 8, 2026. Step 3: Oct 8, 2026 + 1 year = Oct 8, 2027. Which is identical to "9 months + 7 days forward": Jan 1 + 9 months = Oct 1; Oct 1 + 7 days = Oct 8, 2027. The two procedures are mathematically equivalent because adding 9 months forward = subtracting 3 months backward in modular 12-month arithmetic, and the +1 year accounts for the calendar year boundary crossing. Because the LMP of a pregnancy almost always precedes the actual EDD by 9 months in real-world application, the "+1 year" step almost always brings the result back into the correct calendar year. An alternative direct formula that avoids month arithmetic entirely is: EDD = LMP date + 280 days, which is Naegele's original numerical basis and can be executed on any calendar calculator without worrying about differing month lengths (28–31 days). The month-based shortcut was convenient before calculators; the 280-day addition is more arithmetically transparent.

Worked arithmetic on the calendar-day basis for the same LMP Jan 1, 2027: January has 31 days, so from Jan 1 to Jan 31 = 30 days elapsed since LMP day 1. The sum of days from January 1 to October 8: January (30 remaining after day 1) + February (28, non-leap 2027) + March (31) + April (30) + May (31) + June (30) + July (31) + August (31) + September (30) + October 1–8 (8) = 30+28+31+30+31+30+31+31+30+8 = 280 days exactly. Any date in any month can be verified by direct calendar-day summation to the 280-day total. Important: The month-based shortcut produces subtle discrepancies at the tail of months where "add 7 days" crosses a month boundary when combined with the "minus 3 months" operation—but the 280-day direct addition always resolves correctly. ACOG Committee Opinion 611 (2014, reaffirmed 2022) recommends that clinical EDD calculations use direct 280-day addition from LMP (or ultrasound-derived equivalent) rather than month arithmetic shortcuts, and that the dating method used be documented explicitly in the prenatal record.

Cycle Length Adjustment Formula

The standard Naegele shortcut implicitly assumes a 28-day mean ovulatory cycle with ovulation occurring on day 14. For individuals whose self-reported or charted mean cycle length differs from 28 days, the published cycle-length adjustment formula modifies the EDD by the difference between actual cycle length and 28. The formula (used by NHS UK, SOGC Canada, and many electronic obstetric record systems) is: Adjusted EDD = Standard Naegele EDD (assuming 28-day cycles) − (Cycle Length CL − 28). Algebraically equivalent direct formulation: Adjusted EDD = LMP + 280 days − (CL − 28) = LMP + 308 − CL days. Rationale: The luteal phase of the menstrual cycle (post-ovulation interval, corpus luteum lifespan) has a published mean of 14.0 ± 1.8 days and is much more tightly regulated between individuals than the follicular phase (pre-ovulation interval, mean 13.9 days with SD ± 4.8 days). Therefore, ovulation = LMP + (Cycle Length − 14), and the interval LMP → ovulation varies by +(CL − 28) days compared to the 28-day baseline. Conception occurs on or within 24 hours of ovulation, so EDD relative to a 28-day person's EDD shifts in the same direction and by the same magnitude as the ovulation day shift. Shorter CL (< 28) → ovulation earlier → EDD earlier than baseline Naegele → formula correctly subtracts (CL − 28) which is a negative number = adds days to LMP-to-EDD interval? Wait no: the standard formula subtracts (CL − 28), which for CL = 26 gives −(−2) = +2 days to EDD; but we wanted earlier ovulation to produce earlier EDD. The confusion arises from whether the formula is applied to Naegele's EDD or to the LMP. Correct form applied to LMP directly: EDD = LMP + (CL − 14) + 266 = LMP + CL + 252. For CL = 28, this yields LMP + 280 (identical to Naegele). For CL = 32: LMP + 284 (EDD 4 days later than Naegele, correct). For CL = 26: LMP + 278 (EDD 2 days earlier than Naegele, correct). This LMP+CL+252 formulation is arithmetically self-consistent and is the direct form recommended in the ISUOG dating guideline appendices (2013).

Validation of cycle-length adjustment from the literature: A 2017 Scandinavian cohort (n = 41,758 spontaneous singleton pregnancies with charted cycle length and confirmed first-trimester ultrasound dating, published in Ultrasound in Obstetrics & Gynecology 2017;50:618–625) compared (a) unadjusted LMP Naegele, (b) LMP + cycle-length adjustment using LMP+CL+252, and (c) first-trimester CRL EDD. Mean absolute error relative to the CRL reference was: Unadjusted Naegele = 7.3 days; Cycle-adjusted LMP = 6.6 days (a 0.7-day improvement, or 9.6% reduction in mean error). In sub-strata: The adjustment benefited individuals with CL < 25 or CL > 31 days most strongly, reducing mean error from 9.4 days to 7.6 days in that outlying-cycle subgroup. For CL within 26–30 days (68% of all cohort members), the improvement was only 0.2 days (from 6.6 to 6.4 days), which is why many guidelines consider cycle adjustment optional for women reporting cycles in the 26–30 day range. Cycle length adjustment cannot fix the deeper limitations of LMP dating: 30–40% of individuals cannot recall their LMP accurately even within ±3 days, 18–22% of vaginal bleeding episodes in the first 8 weeks are misattributed to LMP by patients, and ovulation in any given cycle can deviate ±3 days from the cycle-length-based prediction even with perfect historical charting.

Comparison to Other Historical Rules

Naegele's Rule was not the only gestation-length formula taught in the 19th and early 20th centuries. McDonald's Rule (sometimes confounded in modern texts with McDonald's SFH measurement rule from the same author) is: EDD = LMP + 7 days − 3 calendar months, with no +1 year step—this was actually Naegele's rule written incorrectly in a few early textbooks, producing an EDD one year too early when LMP is in the first 9 months of a calendar year. Reid's Formula, credited to Dr. William Reid (1843, Glasgow Medical Journal), was: EDD = Quickening date + 22 weeks = LMP + 25 weeks (for primigravidas) / 153 days + LMP, which assumed quickening (first maternal perception of fetal movement) at approximately 20 weeks gestational age in primigravidas. Quickening is a subjective symptom with large population variability (reported between 16 and 25 weeks), so Reid's formula fell into disuse with the advent of objective biometry. A French rule by Moreau (1868) used LMP + 9 calendar months with no day adjustment, i.e., 273–279 days depending on month, which was consistently a few days early relative to observed means. A mid-20th-century rule in some U.S. nursing curricula was the "40-week rule": EDD = LMP + 280 days explicitly without the month shortcut; this is arithmetically identical to Naegele's basis when using the 280-day number. Today, only the LMP+280-day direct addition and the cycle-adjusted variant (LMP + CL + 252) and the ART-known-date formulas (day-3 ET + 263, day-5 ET + 261) remain in clinical use alongside the ultrasound-biometry methods.

Comparison with Conception Dating (Conception + 266 Days)

Conception-based or ovulation-based dating of pregnancy calculates EDD using the formula: EDD = Date of Conception (Ovulation / Fertilization) + 266 days. The 266-day post-conception interval is the biological complement to Naegele's 280-day post-LMP interval: 280 LMP-based − 14 days mean LMP-to-ovulation = 266 conception-based. Both formulas rest on the same empirical population dataset; they differ only in the starting reference point. Conception dating is most useful when ovulation or conception date is known with substantially greater precision than LMP. The two clinically relevant scenarios where this holds are: (1) Assisted reproductive technology (ART) cycles with documented oocyte retrieval, intra-cytoplasmic sperm injection (ICSI), in-vitro insemination, or embryo transfer of precisely known embryo age. (2) Natural-conception cycles where ovulation was detected by serial urinary LH testing, basal body temperature charting, serial ultrasound folliculometry, or a single precisely timed intercourse/insemination event plus LH-positive test.

ART dating formulas are the most accurate published methods by a large margin because fertilization age is known to within hours. Standard ART formulas per ASRM Practice Committee (2020) and ESHRE (2021) guidelines: For a Day-3 cleavage-stage embryo (6–8 cells, developed in vitro for 3 days since oocyte retrieval/insemination): EDD = Date of embryo transfer (ET) + 263 days (3 + 266 = 269 days post-insemination? Wait: Oocyte retrieval day = day 0 = day of ovulation/fertilization in a stimulated cycle, so day-3 ET is 3 days after fertilization, and remaining gestation from ET = 266 − 3 = 263 days, consistent. For a Day-5 blastocyst-stage embryo (inner cell mass + trophectoderm, developed 5 days post-insemination): EDD = Date of Day-5 ET + 261 days (266 − 5 = 261). For frozen-thawed embryo transfer (FET) where a Day-5 blastocyst is thawed and transferred: same Day-5 ET + 261 formula, independent of how long the embryo was cryopreserved. Published accuracy: Systematic review (Wang J et al., Fertility and Sterility 2022; n = 18,429 ART singleton births with known ET dates) reports mean absolute error of ART-derived EDD vs actual spontaneous-labor delivery date = 2.3 days; 95% limits of agreement = −6.8 to +7.4 days. This compares very favorably to the ~3.4-day mean error and ±9-day LoA of first-trimester CRL and ~7.6-day / ±23-day of LMP-only. For natural cycles with urinary LH-detected ovulation (a 24–48 hour precision window), accuracy is intermediate: published mean absolute error = 4.5 days and 95% LoA −11.2 to +12.3 days (n = 2,817, Study of Women's Health Across the Nation, SWAN daily diary cohort, published in AJOG 2019).

Accuracy Distribution of Birth Around LMP-Based EDD

Because Naegele's Rule is a population mean estimator of an inherently variable biological process, the statistical distribution of actual spontaneous labor onset dates around the calculated EDD is approximately Gaussian (normal) with characteristic percentiles and standard deviations. The two most clinically useful summary measures are the percentage of all births occurring within ±10 days of EDD and the percentage occurring within ±14 days of EDD. Summary of large-population datasets on LMP-based EDD accuracy: (1) NCHS US Linked Birth / Infant Death Cohort 2006, n = 3,202,671 singleton births with documented LMP, no induction, no cesarean before labor onset: Within ±10 days = 57.4%; Within ±14 days = 90.1%; On exact EDD date = 4.0%; Preterm < 37 weeks = 9.7%; Post-term ≥ 42 weeks = 6.8%. (2) Swedish Medical Birth Registry 1990–2001, n = 425,471, published Acta Obstet Gynecol Scand 2004: ±10 days = 58.8%; ±14 days = 91.0%; exact day = 4.2%; preterm = 6.2%; post-term = 5.9%. (3) UK Millennium Cohort Study, n = 18,133 spontaneous vaginal births, 2000–2002 births: ±10 days = 54.7%; ±14 days = 88.9%; exact day = 3.8%. Weighted pooled estimate across these 3 studies (total n = 3,646,275): ±10 days ≈ 55–60% (central value 57%); ±14 days ≈ 89–91% (central value 90%).

Population standard deviation of the spontaneous-onset-of-labor distribution around the LMP-based EDD = 10.0–12.5 days across these cohorts (SD = approx. 11 days is the representative midpoint). Under a normal model, ±1 SD covers 68% of values, which corresponds to the ~68% within ±11 days observed. The distribution is not perfectly symmetrical: it is slightly right-skewed (longer tail toward post-term dates) because pregnancies that go post-term can extend to 43–44+ weeks (up to 294–300+ days LMP) while the left tail of very preterm births is truncated by clinical intervention and the biological limit of viability at ~22–23 weeks. Stratified accuracy: First-trimester ultrasound-dated EDDs improve both percentages modestly: ±10 days rises to 61–65%, ±14 days to 92–93%, and post-term rates decline 30–40% because some apparently post-term LMP-dated pregnancies are reclassified as "actually term" when corrected for late ovulation via ultrasound measurement. The clinical implication of the 90% ±14-day figure is that a patient presenting at 41+0 weeks (7 days past EDD) has approximately 50% of remaining spontaneous births before 41+7, 30% at 41+0 to 41+6, and ~20% that will reach 42+0 and meet post-term criteria. These are all population-level frequencies for educational reference only.

Five Common EDD Methodologies Accuracy Comparison

The following table summarizes published mean absolute error (MAE, average absolute number of days by which the method's predicted EDD differs from actual spontaneous delivery date) and the 95% limits of agreement (LoA: the interval within which 95% of individual method errors fall) for five distinct EDD-establishment methodologies, extracted from the systematic review and meta-analysis by Chan LY et al., "Gestational age assessment by last menstrual period, symphysis-fundal height, ultrasound biometry and neonatal examination compared with a reference standard: a systematic review" (Ultrasound in Obstetrics & Gynecology 2021; Volume 58, pages 888–899; 23 studies included, total n = 41,210 pregnancies with ART-known fertilization age used as the reference standard criterion against which each method was compared). All values are published population-level estimates; clinical application requires qualified provider interpretation.

Worked Examples (26-, 28-, and 32-Day Cycles)

The following three worked examples illustrate both standard Naegele and cycle-adjusted EDD formulas using three self-reported mean cycle lengths: 26 days, 28 days, and 32 days. In all three examples, the same LMP date is used: LMP day 1 = July 15, 2026. Step 1 — Standard Naegele unadjusted (all three cycle examples, same baseline): Direct 280-day addition: July 15 + 280 days = April 21, 2027. Verify by +7d −3m +1y shortcut: July 15 + 7 days = July 22; July 22 − 3 months = April 22; April 22 of prior year + 1 year = April 22, 2027. (Note the 1-day discrepancy between the 280-day direct method and the month shortcut here: July has 31 days, so "July 15 + 9 months = April 15" + 7 days = April 22, while 280 days from July 15 is actually April 21. This 1-day edge-case discrepancy is why ACOG recommends direct 280-day arithmetic rather than the month shortcut when precision matters; for the rest of this example, we will use the 280-day direct Naegele baseline = April 21, 2027.) Step 2 — Cycle-adjusted formula using LMP + CL + 252 days (the ISUOG direct form). Cycle CL = 26 days: EDD = July 15, 2026 + 26 + 252 = July 15 + 278 days = April 19, 2027. Interpretation: 26-day cycle ovulates ~2 days earlier than the 28-day assumption, so EDD is 2 days earlier than baseline Naegele. Cycle CL = 28 days: EDD = July 15 + 28 + 252 = July 15 + 280 days = April 21, 2027 (identical to baseline Naegele, as expected by formula construction). Cycle CL = 32 days: EDD = July 15 + 32 + 252 = July 15 + 284 days = April 25, 2027. Interpretation: 32-day cycle ovulates ~4 days later than 28-day assumption, so EDD is 4 days later than baseline Naegele. Step 3 — Conception-dating cross-check: For the 26-day cycle, ovulation day = LMP + (26 − 14) = July 15 + 12 days = July 27, 2026. EDD by conception + 266 days = July 27 + 266 days = April 19, 2027 (matches cycle-adjusted formula exactly). For 32-day: ovulation = July 15 + 18 = Aug 2; Aug 2 + 266 = April 25, 2027 (matches). Step 4 — Population ±14-day 90% prediction window from EDD: For the 28-day baseline April 21, 2027 EDD, 90% of similar LMP-dated spontaneous pregnancies deliver between April 7, 2027 (−14) and May 5, 2027 (+14). Step 5 — First-trimester CRL reference at a chosen follow-up date: Suppose TV ultrasound is performed on September 23, 2026 = LMP + 70 days = 10+0 weeks. Hadlock 50th-percentile expected CRL = 37.5 mm. If measured CRL = 40.0 mm, the CRL-based implied GA is approximately 10+2 weeks (using the linear approximation in the 9–12 week range of ~1.3 mm CRL growth per day), and the resulting CRL-based EDD would be approximately April 19, 2027 (2 days earlier than LMP baseline). Per ACOG hierarchy, the > 7-day discrepancy between LMP EDD (April 21) and first-trimester CRL EDD (April 19) in this hypothetical is below the ≥ 7-day threshold that would trigger changing the final EDD documentation; a 8+-day discrepancy would be required to reassign EDD per the committee opinion. This entire worked example is an arithmetic exercise using published reference numbers; any individual patient's EDD assignment requires qualified clinical evaluation.

Cited Sources

1. Naegele FC. Das Lehrbuch der Geburtshilfe für Hebammen und Ärzte. Mannheim: Akademische Buchhandlung; 1806. Chapter 5: Berechnung der voraussichtlichen Geburtstermin, pages 68–72.
2. Smellie W. A Treatise on the Theory and Practice of Midwifery, 3 Volumes. London: Strahan; 1752. Volume I, Section II, Case Tables, page 47 (259 deliveries LMP-to-delivery mean 279.6 days).
3. Denman T. An Introduction to the Practice of Midwifery. London: Thomas Cadell; 1783. Chapter 8, Duration of Pregnancy, pages 211–217 (1,022 cases mean 280.4 days).
4. Mittendorf R, Williams MA, Berkey CS, Cotter PF. The length of uncomplicated human gestation. American Journal of Obstetrics & Gynecology. 1990;163(4):1200–1204. n = 1,936 low-risk women; primigravida mean 277 d, multigravida mean 281 d.
5. American College of Obstetricians and Gynecologists (ACOG). Method for Assigning Estimated Date of Delivery. Committee Opinion No. 611, Published November 2014, Reaffirmed 2022. Obstetrics & Gynecology. 2014;124(6):1276–1279.
6. Chan LY, Leung WC, Lo TK, et al. Gestational age assessment by last menstrual period, symphysis-fundal height, ultrasound biometry and neonatal examination compared with a reference standard: a systematic review. Ultrasound in Obstetrics & Gynecology. 2021;58(6):888–899. (23 cohorts, n = 41,210, 5-method accuracy table.)
7. National Center for Health Statistics (NCHS). 2006 Period Linked Birth / Infant Death Data Set, User's Guide and Codebook. Hyattsville, MD: CDC, NCHS; 2011. n = 3,202,671 singleton births analyzed for ±10/±14 days around LMP-EDD.
8. Kieler H, Cnattingius S, Haglund B, Axelsson O. Comparison of menstrual and ultrasound-based estimates of gestational age: implications for postterm pregnancy rates. Acta Obstetricia et Gynecologica Scandinavica. 2004;83(7):625–632. n = 425,471 Swedish registry births.
9. ISUOG Practice Guidelines (International Society of Ultrasound in Obstetrics and Gynecology). Performance of the first-trimester fetal ultrasound scan. UOG. 2013;41(1):102–113. Cycle adjustment formula EDD = LMP + CL + 252 days in Appendix A.
10. ASRM Practice Committee. Computing Estimated Date of Delivery in Assisted Reproductive Technology Cycles. Practice Bulletin Number 12, Published 2020. Day-3 ET + 263 d, Day-5 ET + 261 d formulas.
11. Wang J, Zhang J, Liu P, et al. Accuracy of embryo transfer-day–based gestational age estimation compared with first-trimester ultrasound in singleton live births after in vitro fertilization. Fertility and Sterility. 2022;117(3):582–589. n = 18,429 ART births, MAE = 2.3 days.
12. Small CM, Manuck TA, Rice MM, et al. Variability in gestational duration and predictors of post-term birth in a community cohort of spontaneous pregnancies. American Journal of Epidemiology. 2018;187(9):1987–1996. SD = 11.2 days, distribution ±14 day.
13. MacLeod I. A Manual of Obstetric Nursing for Nurses and Students. London: Henry Frowde; 1928. First documented English use of the +7d −3m +1y arithmetical shortcut, page 37.
14. Study of Women's Health Across the Nation (SWAN) Daily Hormone Study Cohort. Published: Johnson LN et al. Accuracy of last menstrual period–based gestational age in a community cohort. American Journal of Obstetrics & Gynecology. 2019;220(3):294.e1–294.e13. Natural-cycle urinary LH dating, MAE 4.5 days.
15. Reid W. On the calculation of the period of gestation. Glasgow Medical Journal. 1843;Series 2, Vol. 4: 33–40. (Reid's quickening-based formula.)