## Wednesday, March 2, 2022

### Measuring Mt Fuji

How Japan’s highest mountain came by its altitude of 3,776 metres

“Mt Fuji is in the province of Suruga: its peak is sculpted as if by a sword-blade, soaring up until it touches the sky,” wrote Miyako no Yoshika (834–879) in the Honchō-monzui, a Heian-era literary compendium, adding that “its height is not to be measured.”

 Survey marker on Mt Fuji's crater rim, c.1901Illustration from Fuji-Annai by Nonaka Itaru (Heibonsha edition)

That was probably good advice at the time, given the wild inaccuracy of early attempts to guess the mountain’s stature. The author of Ise Monogatari, for instance, put it at ten times the height of Kyoto’s Mt Hiei (848m) – or twenty times, these translators say – thus lifting Mt Fuji into the league of the Himalaya’s tallest giants.

Fast-forwarding a few centuries, the savants started to feel the need for more precision. A solid attempt at fixing Mt Fuji’s altitude was made in 1727 by Fukuda Riken. Applying a trigonometrical method from the vicinity of Yoshiwarajuku in what is now Shizuoka Prefecture, he calculated a height of 35.62 chō, equivalent to 3,895 metres,

 Eighteenth-century surveying techniques

Then there was Inō Tadataka (1745–1818), who from the turn of the nineteenth century spent the last seventeen years of his life mapping the whole of Japan – at his own expense. In the process, he made trigonometrical measurements from at least four locations around Mt Fuji’s foot. These resulted in a somewhat scattergun set of estimates. But the altitude he settled on for his map was equivalent to 3,927.7 metres, no more than about 4% off the mark.

Soon devices for gauging air pressure arrived, giving the savants a new way to measure Mt Fuji. The first to deploy such a barometric method was the doctor Ninomiya Keisaku (1804–1862), a colleague or student of Philipp von Siebold (1796–1866). Although it is not known exactly which technique he used, he came up with a height of 3,794.5 metres, extraordinarily close to the modern surveyed altitude. This was in 1828.

In 1860, Rutherford Alcock, her Britannic Majesty’s Minister Plenipotentiary to Japan, became the first foreigner to climb Mt Fuji, together with his dog, Toby. Alcock’s aims during this excursion were mainly political, but as befitted a diplomat who had once trained as a surgeon, he encouraged scientific and botanical observations.

Thus it was that one Lieutenant Robinson came to boil up his thermometer on the summit. Deducing an altitude of 14,177 feet, the naval officer inadvertently promoted Mt Fuji into the ranks of the four-thousand-metre peaks. It is possible that the typhoon which assailed the party soon afterwards might have reduced the air pressure, leading this hypsometrical technique to exaggerate the real height.

More ambitious in his scientific aims was the geographer Ferdinand von Richthofen (1833-1905) – the Red Baron’s uncle – who climbed the mountain in 1870 with Gottfried Wagener (1831-1892). They’d hoped to establish the base point for a magnetic survey, but a lack of preparation prevented them from carrying out their plans. They would not be the last to experience the peculiar challenges of surveying from the top of Japan’s highest mountain.

 Rutherford Alcock's ascent of Fusiyama

A decade later, it was the turn of engineering student-turned-meteorologist Wada Yūji to measure air pressure on Mt Fuji - he took readings at the base while a colleague simultaneously did the same on the summit. Around the same time, the scientist Thomas Mendenhall spent several days on Mt Fuji in August 1880 in order to weigh the earth. Later, “Engineer Wada” was to win fame first as the patron and then as the rescuer of Nonaka Itaru and his wife Chiyoko, who spent 82 days on Mt Fuji in the winter of 1895 to take weather measurements. So it was that humble measurement broke the trail for Mt Fuji’s transformation into a Meizan of science.

Japan’s first official mapmakers – the surveyors of the Army’s general staff – were well aware of the difficulties involved in measuring Mt Fuji. Slant ranges would be hard to measure accurately, owing to the summit’s height above surrounding triangulation points. And this was to say nothing of the problems of coordinating teams of surveyors over such distances. So, wisely no doubt, the government surveyors left Mt Fuji’s summit out of their first network of primary triangulation points, which they laid out in mid-Meiji times.

Of course, the mapmakers couldn’t ignore the summit altogether. So in 1885, they placed a fourth-class triangulation point on Hakusan-dake, a peaklet on the crater rim. From this, the surveyors calculated an altitude of 3,753.4 metres. Then, using a levelling technique (or flat-plate survey), they extrapolated the height of Ken-ga-mine, Mt Fuji’s highest eminence, as 3,778 metres. For more than a generation, this would be the universally accepted height of the mountain.

 Triangulation point on Ken-ga-mine(Photo by courtesy of Nippon no Sokuryoshi)
In 1926, the surveyors went back to Mt Fuji, as part of the government’s initiatives to revive the economy after the Great Kanto Earthquake. This time, they put two new second-class triangulation points on the crater rim, one on Hakusan-dake and another on Ken-ga-mine, the highest point. Two were needed because no single location could be seen from all directions. From the Hakusan triangulation point, the surveyors used the altitude angle measurement method to establish an altitude of 3,776.29 metres for Ken-ga-mine. And this, omitting the decimal fractions, is the source of the summit spot height marked on all current maps of Mt Fuji.

Alas, it is no longer possible to revisit the exact locus of this historical altitude determination. After a decade or so, the rocks around the Ken-ga-mine marker crumbled away, exposing its base. Indeed, the triangulation point itself is rumoured to have tumbled down into the crater below. So, in 1962, the concrete base was rebuilt and the marker adjusted to a height of 3,775.6 metres, or 3,776 metres in round numbers. Erosion also undermined the Hakusan-dake trig point, which also had to be repaired.

Not everybody got swiftly behind the new official altitude. As late as 1943, Dazai Osamu, a literary type, was still referring, in his One Hundred Views of Fuji, to "the three-thousand, seven hundred and seventy-eight-metre mountain…”. Or perhaps the novelist was ahead of the curve. In 2002, Japan’s Geospatial Information Authority of Japan installed the first “electronic reference point” on Ken-ga-mine, giving an altitude of 3777.5 metres.

However, the GIS notes, “this will not change the commonly accepted elevation of 3776 metres.”

References

Uenishi Katsuya, Nippon no sokuryōshi (日本の測量史) website, Surveying Mt Fuji (富士山の測量).

Kamogawa Masashi, “The Mount Fuji Research Station: A Scientific Treasure Trove”, nippon.com

The Nonaka Itaru & Chiyoko Digital Archives (野中 至(到)・千代子資料館), chronology (年 表) for Wada Yūji’s surveying work with Mendenhall in 1880.

Geospatial Information Authority of Japan, Establishment of an electronic reference point on Mt Fuji (富士山に電子基準点設置 －わが国で最も高いところにある基準点).