An ingenious rate clerk named MacGraham, in the offices of the Pennsylvania Railroad, proposed a comprehensive scheme for meeting these difficulties which was first used for westbound rates on December, 15, 1871. The Chicago-New York rate was to constitute a basis, upon which all other rates were to be made in percentages, according to their relative distance from New York.[399] Thus, assuming Chicago to be 900 odd miles from New York, the rate from a point 600 miles inland would be about sixty-six and two-thirds per cent. of the Chicago rate, whatever that might be. Whenever the lake rate at Chicago changed, every other rate throughout trunk line territory would vary in due proportion. Relativity of charges would thus be preserved. Moreover, the shortest route, "worked or workable," was to be used in calculating the rates, the basic distance being about 920 miles by the Lake Shore from Chicago to Dunkirk, Ohio, and thence by the Erie to New York. This would give compelling effect to distance as a factor, and would tend to penalize the roundabout carriage of goods. More than this, however, it would render the inland territory directly tributary to New York. From a point, for example, fifty or one hundred miles south of Chicago, Toledo, or Cleveland, the local rate into those towns plus the through rate east to New York would always exceed the rate by a direct route east. For the hypothenuse of a triangle is clearly always shorter than the sum of the other sides. All shipping points equidistant from New York would enjoy equal rates, those rates at any time being determined by the state of water competition. This was a manifest advantage to the small inland centres, while the rate on the lake front was not affected. The trunk lines lost something, perhaps, through lower rates at intermediate points; but the gain through diversion of traffic from the lake to the rail lines more than compensated. For conditions were such in the summer of 1875 that the lake boats were prepared to carry grain for almost nothing. The railroads were helpless in such cases.[400] The only real sufferers were the short, independent cross lines and the lake and river cities. Of these, the former were reduced to a status of mere feeders or branches of the trunk lines. They were compelled to accede to the plan, however, by threatened refusal of the trunk lines to turn over business to them westbound, unless they reciprocated with their grain shipments eastbound.[401] Many of these lines became bankrupt later, and were absorbed by the larger companies.[402] And, as for the cities unfavorably affected, the scheme based upon distance was so obviously fair that their protests were of no avail.[403]