In Europe, a favorite method of aiding science is to offer a prize for the best memoir on a specified subject.  On theoretical grounds this is extremely objectionable.  Since the papers presented are anonymous and confidential, no one but the judges know how great is the effort wasted in duplication.  The larger the prize, the greater the injury to science, since the greater will be the energy diverted from untried fields.  It would be much wiser to invite applications, select the man most likely to produce a useful memoir, and award the prize to him if he achieved success.

The award of a medal, if of great intrinsic value, would be an unwise expenditure.  The Victoria Cross is an example of a successful foundation, highly prized, but of small intrinsic value.  If made of gold, it would carry no greater honor, and would be more liable to be stolen, melted down or pawned.

Honorary membership in a famous society, or honorary degrees, have great value if wisely awarded.  Both are highly prized, form an excellent stimulus to continued work, and as they are both priceless, and without price, they in no way diminish the capacity for work.  I recently had occasion to compare the progress in various sciences of different countries, and found that the number of persons elected as foreign associates of the seven great national societies of the world was an excellent test.  Eighty-seven persons were members of two or more of these societies.  Only six are residents of the United States, while an equal number come from Saxony, which has only a twentieth of the population.  Of the six residents here, only three were born in the United States.  Not a single mathematician, or doctor, from this country appears on the list.  Only in astronomy are we well represented.  Out of a total of ten astronomers, four come from England, and three from the United States.  Comparing the results for the last one hundred and fifty years, we find an extraordinary growth for the German races, an equally surprising diminution for the French and other Latin races, while the proportion of Englishmen has remained unchanged.

A popular method of expending money, both by countries and by individuals, is in sending expeditions to observe solar eclipses.  These appeal both to donors and recipients.  The former believe that they are making a great contribution to science, while the latter enjoy a long voyage to a distant country, and in case of clouds they are not expected to make any scientific return.  If the sky is clear at the time of the eclipse, the newspapers of the next day report that great results have been secured, and after that nothing further is ever heard.  Exceptions should be made of the English Eclipse Committee and the Lick Observatory, which, by long continued study and observation, are gradually solving the difficult problems which can be reached in this way only.

The gift of a large telescope to a university is of very doubtful value, unless it is accompanied, first, by a sum much greater than its cost, necessary to keep it employed in useful work, and secondly, to require that it shall be erected, not on the university grounds, but in some region, probably mountainous or desert, where results of real value can be obtained.