This document is part of my discussion of the Decline of the Lifespans of the Númenóreans.  Please cite this essay if you quote it or use it.  You can e-mail me.

 

Estimating the Lifespans of the Númenórean Kings

 

This is a simple way to estimate the lives of the Númenórean Kings.  The purpose of this exercise is to begin to estimate the lifespans of the Lords of Andúnië, and to try to shed some light on what Tolkien might have been doing when he set up his own tables as time went on.

 

Stating in column A, type in numbers 1 to 25.  That’s the order of the kings: there were 25, excluding Anducal, the usurper. 

 

In column, B, put in the ages of the kings.  You can look them up or take them from my earlier post.

 

In column C, put in 500 for the estimated age of the first king.  Then put in 405 for kings 2 through 13.  Beginning with king 14, take off 5.75% of the age of the previous king, and do that all the way to king 25.  (The easiest way to do this is to multiply the estimated age of the king above by 0.9425, or 1 – 5.75%.)

 

Plot columns A, B, and C.  If you use a line plot, A will become the x-axis.  The data in Columns B and C line up very nicely. 

 

If you want to see how much the estimate is off the actual, at the top of Column D (in cell D1), type in

=(c1-b1)/b1

That will give you the percent error of the estimate.  Copy it into cells D2 to D25.  Calculate the average (that is, =average(d1:d25) ), and you should get -0.29%. 

 

This is very easy to do in a spreadsheet, but it’s very tedious to do by hand.  That’s why I suggested Tolkien might have done this by graphing it.  That way, he could just read the results off the graph, and of course, they’d always be just a little off the actual number.  He didn’t have to use graph paper: if he was careful, he could have sketched it and gotten these results.

 

The average reign of a ruler should be same as the average time between generations.  Elros was king longer than anyone else, and Vardamir was in fact never king at all (despite the “official” record that he reigned one year).  For the next 11 kings, the average reign is 160 years, and so is the average length of time between generations.  If you start with birth of Vardamir and add 160 years, you can get a good estimate of the birth year of the next 11 kings. 

 

Starting with Ancalimon, the 14th king, the reign of each king begins to shorten.  Because the preceding king (each person’s father) outlives him, the length of each reign falls faster than the lifespan of each king.  You can approximate this rate using a decline of –6.25%.  Doing this, you can continue to add reigns/generations to each birth year until you arrive at king 25, Pharazôn, and get an estimate of 3114 for his birth year.  The year Tolkien used (in the version of the story I used to build the model) is 3118. 

 

 

 

 

King

age

est. age

age error

ruled

target reign

error reign

born

target birth

error birth

age father

sovereign

age to rule

target sov.

error sov.

Retired

died

target death

error death

1

Elros

500

500

0.00%

 

 

 

-58

 

 

119

32

 

 

 

442

442

442

0.00%

2

Vardamir

410

405

-1.22%

 

 

 

61

60

 

131

442

 

 

 

443

471

 

 

3

Amandil

411

405

-1.46%

148

160

8.11%

192

220

 

158

442

200

420

-4.98%

590

603

600

0.50%

4

Elendil

401

405

1.00%

150

160

6.67%

350

380

 

193

590

200

580

-1.69%

740

751

785

-4.53%

5

Meneldur

399

405

1.50%

143

160

11.89%

543

540

0.55%

157

740

200

740

0.00%

883

942

945

-0.32%

6

Aldarion

398

405

1.76%

192

160

-16.67%

700

700

0.00%

173

883

200

900

1.93%

1075

1098

1105

-0.64%

7

Ancalimë

412

405

-1.70%

205

160

-21.95%

873

860

1.49%

130

1075

200

1060

-1.40%

1280

1285

1265

1.56%

8

Anárion

401

405

1.00%

114

160

40.35%

1003

1020

-1.69%

171

1280

200

1220

-4.69%

1394

1404

1425

-1.50%

9

Súrion

400

405

1.25%

162

160

-1.23%

1174

1180

-0.51%

146

1394

200

1380

-1.00%

1556

1574

1585

-0.70%

10

Telperiën

411

405

-1.46%

175

160

-8.57%

1320

1340

-1.52%

154

1556

200

1540

-1.03%

1731

1731

1745

-0.81%

11

Minastir

399

405

1.50%

138

160

15.94%

1474

1500

-1.76%

160

1731

200

1700

-1.79%

1869

1873

1905

-1.71%

12

Ciryatan

401

405

1.00%

160

160

0.00%

1634

1660

-1.59%

166

1869

200

1860

-0.48%

2029

2035

2065

-1.47%

13

Atanamir

421

405

-3.80%

192

160

-16.67%

1800

1820

-1.11%

186

2029

189

2009

-1.01%

 

2221

2225

-0.18%

14

Ancalimon

400

382

-4.57%

165

150

-9.09%

1986

1970

0.81%

150

2221

178

2148

-3.30%

 

2386

2352

1.44%

15

Telemmaitë

390

360

-7.75%

140

141

0.45%

2136

2111

1.19%

141

2386

167

2278

-4.52%

 

2526

2470

2.20%

16

Vanimeldë

360

339

-5.81%

111

132

18.77%

2277

2242

1.52%

129

2526

158

2400

-4.98%

 

2637

2582

2.10%

17

Alcarin

331

320

-3.45%

100

124

23.60%

2406

2366

1.66%

110

2657

149

2515

-5.35%

 

2737

2686

1.88%

18

Calmacil

309

301

-2.52%

88

116

31.67%

2516

2482

1.35%

102

2737

140

2622

-4.20%

 

2825

2783

1.48%

19

Ardamin

281

284

1.03%

74

109

46.80%

2618

2591

1.05%

91

2825

132

2723

-3.62%

 

2899

2874

0.85%

20

Adûnakhôr

253

268

5.76%

63

102

61.65%

2709

2692

0.61%

89

2899

125

2817

-2.83%

 

2962

2960

0.07%

21

Zimrathôn

235

252

7.31%

71

95

34.47%

2798

2788

0.36%

78

2962

117

2905

-1.92%

 

3033

3040

-0.23%

22

Sakalthôr

226

238

5.17%

69

90

29.72%

2876

2877

-0.05%

84

3033

111

2988

-1.48%

 

3102

3115

-0.42%

23

Gimilzôr

217

224

3.23%

75

84

11.88%

2960

2961

-0.04%

75

3102

104

3066

-1.17%

 

3177

3185

-0.26%

24

Palantir

220

211

-4.03%

78

79

0.86%

3035

3040

-0.16%

83

3177

98

3138

-1.22%

 

3255

3251

0.12%

25

Pharazôn †

201

199

-1.00%

64

74

15.24%

3118

3114

0.14%

 

3255

93

3206

-1.50%

 

3319

3313

0.19%

 

average

 

 

-0.29%

 

 

12.34%

 

 

0.11%

 

 

 

 

-2.27%

 

 

 

-0.02%

 

 

Now you can set a similar spreadsheet for the Lords of Andúnië.  Substitute Silmariën for her brother Meneldur, and Valandil for his cousin Aldarion.  You’ll need another column to count the Lords of Andúnië; Valandil is the first one.  Knock out all the names until you get to the 15th lord: that’s Eärendur.  The 16th lord is not named; the 17th is Numendil, the 18th Amandil, and the 19th would have been Elendil, who went to Middle-earth.  You will notice that you have 2 fewer generations than in the line of the kings.

 

The goal here is to find the correct ratios of: (1) the shrinkage of the lifespans and (2) the length of the reigns; in order spread out the lines of the Lords of Andúnië to get a good estimate of the assigned birth-year for Elendil, 3119.

 

Non-sequitur:  Just as Ar-Pharazôn is one year older Elendil, Denethor II is one year older than Aragorn.  Perhaps that’s another bad-king/good-king pair, and perhaps this is more than coincidence; although I’m not sure Tolkien intended any such inference.  I really don’t consider Denethor a wicked person by any means.  Even if Tolkien intended such an inference – that is, Ar-Pharazôn: Elendil::Denethor:Aragorn – I have no idea how anyone could demonstrate that linkage without some explicit statement or reasonably clear discussion on the part of Tolkien himself.  It’s just a non-sequitur.

 

 

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