The man must have a compass in his eye, as the saying goes; that was all.
Uncle Prudent stuck in his needle at the same moment as Phil Evans did his.

Then there began the measurement to discover which of the two competitors had most nearly approached the center.
Wonderful! Such had been the precision of the shots that the measures gave no appreciable difference.

If they were not exactly in the mathematical center of the line, the distance between the needles was so small as to be invisible to the naked eye.
The meeting was much embarrassed.
Fortunately one of the members, Truck Milnor, insisted that the measurements should be remade by means of a rule graduated by the micrometrical machine of M.Perreaux, which can divide a millimeter into fifteen-hundredths of a millimeter with a diamond splinter, was brought to bear on the lines; and on reading the divisions through a microscope the following were the results: Uncle Prudent had approached the center within less than six fifteenth-hundredths of a millimeter.

Phil Evans was within nine fifteen-hundredths.
And that is why Phil Evans was only secretary of the Weldon Institute, whereas Uncle Prudent was president.

A difference of three fifteen-hundredths of a millimeter! And on account of it Phil Evans vowed against Uncle Prudent one of those hatreds which are none the less fierce for being latent..