How better to understand the terrible calculus that went into the decision of President Harry S. Truman to order the dropping of nuclear weapons on two Japanese cities on August 6 and 9, 1945, than to read the basic documents, all (unless otherwise indica ted) from the Harry S. Truman Library in Independence, Missouri?

In the mind of the president of the United States were surely two reasons for using these new and, as it turned out, enormously destructive weapons. One was of course the way in which the Japanese armed forces, principally the Japanese army, had conduc ted World War II. The barbarities of the war had their beginnings in Japan's war against China, which began in 1937. That same year, when Japanese troops occupied Nanking, the human cost was extraordinary: Between 100,000 and 200,000 people were killed by the occupying troops for no reason at all except what may only be described as blood lust.

Years later, after the end of World War II, the responsible Japanese commander, General Iwane Matsui, was arraigned before a war crimes tribunal in Tokyo and subse quently sentenced and hanged. His excuse for what had happened was that he had not known what was going on; the excuse of ignorance could not, however, absolve him of the responsibility he bore. In the war crimes trials after the war, it was impossible to seize upon subordinate commanders, both for what was described as "the rape of Nanking" and other countless horrors that marked Japanese army actions in China before American entrance into the war on December 7' 1941.

And then there was the event that brought the United States into the war. The "sneak attack"-without a declaration of war-by Japanese carrier planes upon Pearl Harbor resulted in the deaths of 1,000 men on the battleship U.S.S. Arizona, which sank so rapidly that the sailors sleeping below deck could not escape, and nearly 1,500 other deaths aboard ships in the harbor, on the surrounding airfields, and among civilians caught in the machine-gun fire and exploding bombs.

Pearl Harbor was not the only instance of Japanese barbarism that Americans knew. It was followed by the Bataan death march beginning April 9, 1942, during which 72,000 exhausted Filipino and American defenders of the Bataan peninsula were marched for four days a distance of 5O miles without food and water, while Japanese soldiers shot or bayoneted hundreds of stragglers. And there were, in addition, the bestial conditions in the Japanese prison camps endured by military prisoners and interned civilians for the remainder of the war-three and one-half years. And the innumerable instances (seemingly random but nonetheless displaying the Japanese army's contempt for prisoners) of shootings and beheadings that continued until the end of World War II.

All of the above, moreover, were instances of maltreatment of only American prisoners; these instances were multiplied into the tens of thousands when one considered British, Dutch, and other Allied prisoners taken mostly in the war's first months at Hongkong, Singapore, the Dutch East Indies, and in Burma.

Japan's conduct of the war, in violation of the Geneva conventions drawn up in a series of international meetings but affixed most recently in international law during the mid-1920s, was akin to Nazi Germany's treatment of Soviet prisoners during the war and of the Holocaust itself, the genocides that came out of Germany's appalling racial policies under the Nazi regime.

And then, in calculating why President Truman and leading officials of his administration looked upon nuclear warfare as a positive good rather than terrible savagery, there was the very real issue in the summer of 1945 of the cost of a U.S. invasion of the Japanese home islands. Whatever the historical-one might describe them as emotional-reasons for "getting back at" Japan, there was the frightening cost of an invasion by the U.S. Army and Navy.

It might seem to an onlooker or casual observer that any calculation of an invasion at that time (an invasion that in fact never took place) was so speculative and so likely to partake of estimates and generally of unreality that it was incalculable, that the contemplated invasion was largely theory rather than actuality and that there was thereby no basis on which to make the decision that the president and his advisers did ultimately make, namely, to risk (and, in fact, this is what happened) the deaths of 100,OQO or more Japanese, including many, many civilians-men, women, and children. But the calculus was not at all theory, for there was clear evidence that an invasion would be enormously costly. In retrospect it is improper to say that Truman and his principal assistants took their momentous decision largely out of emotion, memory of Japanese bestialities, and without serious measurement of what the U.S. forces might be up against.

The two benchmarks for the possible cost of invading the home islands were the American invasions of Iwo Jima and Okinawa in the spring and early summer of 1945.

The invasion of Iwo proved extremely costly: 6,200 U.S. Marines died on that small island that was so valuable as an airbase for B-29s involved in the bombing of Japan. Some of the bombers that were unable to make their runs or upon return were crippled by antiaircraft or other damage or mechanical failures, were able to land there.

The American preponderance over the Japanese defenders at Iwo Jima was four to one. The invasion of the large island of Okinawa, which was 350 miles south of the southernmost home island of Kyushu, proved twice as costly: 13,000 died, one-third of them aboard ship as a result of the dozens of kamikaze attacks. The pilots of these outmoded planes, which often had no ability to get back to their bases, sacrificed themselves and their planes as bombs. In the single most costly kamikaze attack (on the big carrier U.S.S. Franklin), the cost in U.S. deaths was 1,000 men, and the attack turned the ship into a flaming near-wreck, useless for any further campaigns.

While this carnage was taking place, the Marine and army troops on Okinawa were fighting across the island foot by foot, encountering the defenders who battled until they died. The entire Japanese high command committed hara-kiri. The civilian populace meanwhile served as beasts of burden and frequently as cannon fodder: They were driven ahead of Japanese lines to take the initial fire of the Americans and to detonate mines along the way. American casualties-wounded, missing, and dead-totaled 35 percent of the attacking force, despite the preponderance of U.S. ground forces of two and one-half to one.

By mid-June 1945, the huge question in the minds of American commanders and members of the Truman administration was whether it was possible to persuade the Japanese government and military to surrender. The Japanese military (though clearly beaten) was not willing to surrender. If the decision could have been made by Japan's civilian leaders or even the Japanese people, the war probably would have come quickly to an end, but unfortunately the decision was not theirs: It lay in the hands of the military, and particularly in the hands of army leaders. (By this time the Japanese Navy had virtually ceased to exist, almost all its ships having become either unserviceable or having been sunk.)

Leaders of the Japanese army had decided to fight on, whatever the cost, and thereby honor the Japanese military code of bushido, that of warriors whose careers might be traced back to the distant past. That the struggle, in the early summer of 1945, could not be waged in the manner of past struggles-through man to man clashes-but had to be fought in the twentieth-century manner with weapons, did not concern the Japanese military leaders. They would fight with whatever lay at hand. And the defensive weapons they did have, which was an array of artillery pieces and about 5,000 planes that could be used as kamikazes, were bound to cost the attackers heavily, as on Iwo Jima and Okinawa.

By mid-June American military leaders were becoming fearful of what their military services might be up against, and calculations of a tentative sort were made, all of them frightful in their implications. A joint war plans committee, army and navy, came up with an estimate that 25,000 men would be killed in an invasion of Kyushu on two fronts; 40,000 might die if an invasion on a single front was followed by invasion of the island of Honshu, on which Tokyo was located; and 46,000 deaths were estimated as a result of a two-front invasion of Kyushu followed by an invasion of Honshu.

These figures, however, were so tentative that the army's chief of staff, General George C. Marshall, did not discuss them or even mention them during a White House meeting on June 18, 1945. Instead Marshall rather confusedly said that he thought an invasion might not be more costly than the invasion of the Philippine Island of Luzon, which in its first thirty days accounted for a little more than 1,000 casualties per day- that is, 31,000 casualties (wounded as well as dead, the latter usually amounting to one-fourth of the casualties). Marshall apparently advanced this figure with little or no thought, for the Japanese commander on Luzon, General Tomoyuki Yamashita, had pulled back his force during the first month of the invasion so as to avoid naval gunfire, and the fighting thereafter had been much more deadly.

A more likely figure for casualties was advanced at this meeting by President Truman's personal chief of staff, Admiral William D. Leahy, who said that he thought casualties in an attack upon Kyushu and Honshu would be about the same as on Okinawa-that is, about 35 percent of the U.S. attacking force. During this discussion the president remarked his horror at the possibility that an invasion would amount to another Okinawa from one end of Japan to the other.

Any careful contemplation of the cost of an invasion would have shown a horrendous number of American casualties, as the attendees at the June 13 meeting knew, even though they did not make their points - even Leahy failed to say precisely the casualties he had in mind - as carefully as they should have. If Leahy had extrapolated for the force the U.S. Army was proposing to put on Kyushu, he would have related a figure for casualties that would have been more than one-third of 767,000, that is, more than 250,000 casualties. And if one calculated the deaths from the casualties it would have been (figuring that the American troop strength on Okinawa had been as high as 150,000, with deaths running to 13,000, as mentioned) five times the Okinawa figure, which meant 65,000.

And there was another figure that needed to be taken into consideration: the Japanese troop strength on Kyushu. In the invasions of Iwo Jima and Okinawa the U.S. forces always had had a preponderance, respectively four times to one and two and one-half times to one. In mid-June General Marshall had estimated Japanese strength on Kyushu at 350,000. By July 24 he was saying 500,000, and by August 6 his figure rose to 560,000. He was drawing these figures from the analysis by intelligence of Japanese radio traffic, an operation known as Ultra. What he did not know was that Ultra's estimates were unduly low and that by August 6 the Japanese force on Kyushu had reached 900,000. The invasion of Kyushu was scheduled for November 1, and by that date Japanese troop strength on Kyushu could well have been over 1 million, which meant that U.S. invasion forces would be heavily outnumbered.

Moreover, the danger from kamikazes, so readily apparent during the Okinawa operation, would have been much more serious in the Kyushu invasion; the kamikazes had had to fly south to Okinawa from Kyushu, but would have to fly almost no distance before meeting the attackers on Kyushu itself. A single successful kamikaze attack on a large American ship, such as the U.S.S. Franklin , or on a troopship, could have raised the U.S. death toll markedly.

All this, then, was the calculus as American officials, from the president on down, sought single-mindedly to save the lives of U.S. soldiers and sailors during the crucial days and weeks in the summer of 1945. As one may well imagine, they were willing to take almost any measure to end what had become a fight to the finish against the forces of Imperial Japan.