The o-yatoi who weighed the earth

A mid-Meiji encounter of science and religion at the summit of Mt Fuji

On a windy day in early August 1880, the priest called Kinoshita lost his sacerdotal cool. Half an hour ago, a balding foreigner had asked him, through an interpreter, if he could set up his infidel devices in Kinoshita's shrine - the Summit Sanctuary of the Sengen Goddess of Mt Fuji herself.

SUNSET FROM THE SUMMIT OF FUJI -- The Photographer Catches His Shot At the End of a Long Climb, a photo by Okinawa Soba on Flickr.

Unthinkable, fumed Kinoshita, as he sent the interlopers on their way. Yet now the interpreter, this gangling student-type, was coming over to pester him again. Would the estimable priest be so good as to reconsider his decision, the student was asking, because the American sensei wants to weigh the earth.

Thomas Corwin Mendenhall (left) did not come to Japan specifically to weigh the earth. As one of the 3,000 or so 'o-yatoi' or foreign employees of the Meiji government, he'd been invited to teach physics at the newly established Tokyo Imperial University. Arriving in Yokohama on September 21, 1878, he gave his first lecture the very next day, from a podium set up in a venerable Buddhist temple. (The images had been carefully moved aside for the occasion).

Mendenhall attached great weight to the experimental method. Experiments, you could say, were the making of him. Born in 1841, the youngest of five children, he was brought up on a farm in eastern Ohio. It was a young Quaker teacher, teaching through practical demonstration, who started him on the road to science. For instance, during recess, the girls' shawls were used to block out the windows. A pinhole in this screen produced a clear image of children playing outside, projected onto the room's white ceiling.

Money was scarce; the future physicist had to buy his copy of Euclid with a silver dollar he earned by driving a neighbour's cow twenty-five miles to market. The only way he could get a further education was to become a teacher, which he did by taking his teaching certificate at the age of sixteen. From his first job at a primary school, he worked his way up to a professorship at the new Ohio Agricultural and Mechanical College (now Ohio State University) in 1873. Then came the invitation to Japan.

Once in Tokyo, Mendenhall built, more or less from scratch, a modern physics laboratory, using equipment sent from friends in America; all his students would be required to do lab work. Some would also accompany him on field trips and take part in research projects.

It is unclear how Mendenhall lit on the idea of measuring the earth's gravity on the summit of Mt Fuji. Perhaps the idea came to him when the "most beautiful mountain in the world" had soared over the sea horizon, as if to welcome him, the day before his ship docked in Yokohama.

As for the apparatus, he'd become interested in measuring gravity by means of pendulums. A fellow o-yatoi, Professor Chaplin, the professor of civil engineering at Todai, lent him an astronomical transit instrument, by which the accuracy of the recording chronometers could be checked. Now all was set.

The scientists and their instruments travelled to the foot of Mt Fuji, by jinrikisha - the railway went only as far as Yokohama. The students had gone ahead to make arrangements. As the Americans arrived in Subashiri at night, it was not until next morning that the great volcanic peak revealed its full splendour. At which, Professor Chaplin turned to Mendenhall and exclaimed, "My God, I don't wonder they worship it."


At 8am, the party started its ascent. One of the "goriki" or porters had to carry the main part of the transit instrument, which weighed 160 pounds, but he still managed to outclimb the two scientists. By mid-afternoon, in the barren wastes of scoria above the treeline, they were struggling. And the summit still looked far away.

Just then, the Americans were overtaken by a band of pilgrims, all dressed in flowing robes of white, their leader urging them on with a small bell. Mendenhall noted that the leader limited each effort to one hundred steps, which he counted in a loud voice. After each advance, the pilgrims fell instantly to the ground, where they rested under their immense straw hats, until called to their feet again by the leader's bell.

PILGRIMS DESCENDING FUJI, a photo by Okinawa Soba on Flickr.

The pilgrims didn't seem to pay much attention to their leader's counting - instead, they timed their paces to their chanting of the mountain votary's prayer - "Rokkon, shōjō" (May our six senses be purified). The scientists fell in with this group, learned their chant, shared their climbing routine, and had their moral support through the rest of that day.

They put up for the night at a hut near the eighth station, where they admired the mountain's conical shadow as it stretched out further and further until the sun finally set. The pilgrims too stayed in this hut, yet all managed a comfortable night.

Next day, the scientists reached the summit. They soon found an adversary that they hadn't reckoned with - the strong wind that prevented them from putting up their tents. And even if somehow the tents could have stayed up, the blustering gusts would have disturbed the instruments too much for useful readings.


What to do? They peered down into the sheltered crater - perhaps three hundred feet deep, by Mendenhall's guess - but the difficulties of getting the instruments down its stone-raked walls looked insurmountable. It was then that they decided to ask the priest in charge of the summit shrine if they could use his main sanctuary as a temporary laboratory.

The scientists' first request was rebuffed - the priest seemed indignant even to be asked. Mendenhall decided to give him half an hour to recover his composure, then resolved to make another trial. This time the scientist explained, through one of the students, that his experiment was intended to compute the weight of the earth.

Signs of interest appeared on the priest's face and soon he agreed to lend his shrine to the scientists for three or four days. In a few hours all was ready: the image of Buddha was respectfully moved to the back of the hut, the pendulums were mounted on stones projecting from the walls, the chronograph was connected with the chronometer and set going, and the transit instrument was deployed near the door, ready to take star sightings.

Mendenhall's experiment drew on an illustrious heritage. It was Isaac Newton, no less, who was the first to hazard a guess at the earth's density. You'll find it in the Principia, Book III, The System of the World, Proposition 10, Theorem 10:

Accordingly, since the ordinary matter of our earth at its surface is about twice as heavy as water, and a little lower down, in mines, is found to be about three or four or even five times heavier than water, it is likely that the total amount of matter in the earth is about five to six times greater than it would be if the whole earth consisted of water, especially since it has already been shown above that the earth is about four times denser than Jupiter.

This was a prescient conjecture. But it still had to be verified in the hard currency of experimental results. The baton was taken up about half a century after Newton's death by Britain's Royal Society, which set up a so-called Committee of Attraction.

In 1774, this body sent Nevil Maskelyne, the Astronomer Royal, to visit a 3,500-foot mountain in Scotland. By measuring how far the mountain attracted a plumb line away from the vertical, the savants would be able to calculate by how much the earth's attraction outweighed, so to speak, that of the mountain.

The Fairy Hill of the Caledonians - Schiehallion, a photo by idg on Flickr.

Schiehallion, the mountain in question, was chosen for the Fuji-like regularity of its conical form. This, it was hoped, would simplify the task of estimating the mountain's density, on which the whole calculation depended. It may be that Schiehallion's form wasn't sufficiently Fuji-like; Maskelyne's result came in one-fifth too low, making the earth rather too light.

It fell to Henry Cavendish, another Committee of Attraction member, to perfect an indoors experiment. This would eliminate the geological guesswork, by measuring the gravitational pull of one lead sphere on another. The apparatus was so sensitive, indeed, that readings had to be taken through a telescope, from outside the sealed-off laboratory.



Published in 1798, Cavendish's paper puts the earth's density at 5.48 times that of water. It was Cavendish too who first wrote of "weighing the earth" - the earth's mass can, of course, be deduced from its density. In this way, he unwittingly coined the phrase that would later win over priest Kinoshita on the summit of Mt Fuji.

Twenty or so years later, another savant caught a slip in Cavendish's arithmetic - the actual result from his apparatus should have been 5.45. Nobody said that weighing the earth was going to be easy.

Mendenhall's experiment drew on work by later British and European scientists who used pendulums to take gravity readings both on the surface and at the bottom of deep mine-shafts. The idea was to find the difference between the two different gravity readings; the pendulum should swing slightly faster in the stronger gravitational field underground than it would on the surface.

Then, knowing the radius of the earth and knowing (or at least guessing) the density of the ground between the surface and the depths of the mine, you could educe the density of the whole earth. The method was pioneered by the British astronomer George Airy, not without tribulation. His first attempt, in 1826, failed after one of the pendulums met with an accident; a second try miscarried when the mine flooded.

The experiment was eventually completed in 1854, Airy's pendulum swinging just over two seconds per day faster below ground than above. After taking the advice of a mineralogist on the density of the overlying rock, Airy concluded that the earth weighed slightly more than six and half times heavier than the equivalent volume of water.

Mendenhall's innovation was to substitute a mountaintop for the mineshaft. Using self-devised pendulums for greater accuracy, he took readings first in Tokyo, then on Fuji, and then in Tokyo again. The mountaintop work was favoured by clear days and starry nights for the transit readings.


When the country below was covered in cloud, the scientists felt as if they were floating on an island in the sky. The pilgrims, apparently undisturbed, kept filing up to the shrine to make their obeisances and throw copper coins in at the door. One of the students collected up these offerings and took them to the priest.

When it came to estimating the volcano's density, Mendenhall went one better than Airy; he polled five different geologists and averaged their opinions. If Mt Fuji were 2.12 times denser than water - the mean estimate of the geologists - then the earth's density would be 5.51, Mendenhall calculated.

Announced the following year in a lecture "on pendulum experiments on the summit of Fujiyama", this result came within a hair of the currently accepted value.

SAILING INTO FUJI, a photo by Okinawa Soba on Flickr.

The following summer, the Mendenhalls sailed for home, catching a final glimpse of Mt Fuji from the ship's rail. Successful as the gravity experiments had been, the professor saw his students as his principal legacy. "Always fond of teaching," he wrote later, "I cannot but look back upon my three years with these well-mannered, good tempered, ambitious, and intellectually strong men as being ... the pleasantest and best of all my professional years."

The ambitious young men bore out their promise. One, Kikuchi Dairoku, went on to become a minister of education and, briefly, the first president of RIKEN, Japan's government-sponsored science research institute. Another, Tanakadate Aikitsu (standing, second from right in photo), made important discoveries in geophysics.

Quite probably it was Tanakadate (left), a north-country samurai, who handled the delicate negotiations with the priest of Mt Fuji's summit shrine. If so, he made a good impression. Just before the scientists left the mountaintop - a dense fog had rolled in, spoiling the view - Mendenhall sought out the priest who had made his experiment possible.

The professor wanted to express his gratitude with a generous sum of money but the priest refused all reward; it was an honour, he said, to have been able to help in the solution of such an interesting problem. Since then, wrote Mendenhall in his memoirs, "I have always taken much pleasure in naming this liberal-minded Japanese, named Kinoshita, who allowed me to transform a holy shrine of almost the oldest of religions into a laboratory of science and to substitute for his sacred images the most recent devices for the measurement of time."

Science and religion often came to blows in the second half of the nineteenth century. Yet, for a few days in August 1880 atop Mt Fuji, they achieved an amicable and productive cooperation.

References

Crew, Henry, Biographical memoir of Thomas Corwin Mendenhall, National Academy of Sciences, 1934

Dickey, John S, On the rocks: earth science for everyone, 1996.

Hughes, David W, The mean density of the earth, Journal of the British Astronomical Association, 1.2006 - and many thanks to Professor Hughes for kindly providing an explanation of how the Airy experiment worked.

Mendenhall, T C (Jr.) (1989) American Scientist in Early Meiji Japan: The Autobiographical Notes of Thomas C. Mendenhall

Mendenhall, T C, On pendulum experiments on the summit of Fujiyama for the purpose of ascertaining the force of gravity at that point, Abstract of lecture read October 20th, 1881