_Answer._-- If the shot should preserve continuously its initial velocity of 12,000 yards per second, it would require little more than nine hours to reach its destination; but, inasmuch as that initial velocity will be continually decreasing, it will occupy 300,000 seconds, that is 83hrs. 20m. in reaching the point where the attraction of the earth and moon will be _in equilibrio_. From this point it will fall into the moon in 50,000 seconds, or 13hrs. 53m. 20sec. It will be desirable, therefore, to discharge it 97hrs. 13m. 20sec. before the arrival of the moon at the point aimed at.
Regarding question _four_, "At what precise moment will the moon present herself in the most favorable position, etc.?"_Answer._-- After what has been said above, it will be necessary, first of all, to choose the period when the moon will be in perigee, and _also_ the moment when she will be crossing the zenith, which latter event will further diminish the entire distance by a length equal to the radius of the earth, _i. e._3,919 miles; the result of which will be that the final passage remaining to be accomplished will be 214,976 miles. But although the moon passes her perigee every month, she does not reach the zenith always _at exactly the same moment_. She does not appear under these two conditions simultaneously, except at long intervals of time. It will be necessary, therefore, to wait for the moment when her passage in perigee shall coincide with that in the zenith. Now, by a fortunate circumstance, on the 4th of December in the ensuing year the moon _will_ present these two conditions. At midnight she will be in perigee, that is, at her shortest distance from the earth, and at the same moment she will be crossing the zenith.
On the _fifth_ question, "At what point in the heavens ought the cannon to be aimed?"_Answer._-- The preceding remarks being admitted, the cannon ought to be pointed to the zenith of the place. Its fire, therefore, will be perpendicular to the plane of the horizon;and the projectile will soonest pass beyond the range of the terrestrial attraction. But, in order that the moon should reach the zenith of a given place, it is necessary that the place should not exceed in latitude the declination of the luminary; in other words, it must be comprised within the degrees 0@ and 28@ of lat. N. or S. In every other spot the fire must necessarily be oblique, which would seriously militate against the success of the experiment.
As to the _sixth_ question, "What place will the moon occupy in the heavens at the moment of the projectile's departure?"_Answer._-- At the moment when the projectile shall be discharged into space, the moon, which travels daily forward 13@ 10' 35'', will be distant from the zenith point by four times that quantity, _i. e._ by 52@ 41' 20'', a space which corresponds to the path which she will describe during the entire journey of the projectile.
But, inasmuch as it is equally necessary to take into account the deviation which the rotary motion of the earth will impart to the shot, and as the shot cannot reach the moon until after a deviation equal to 16 radii of the earth, which, calculated upon the moon's orbit, are equal to about eleven degrees, it becomes necessary to add these eleven degrees to those which express the retardation of the moon just mentioned: that is to say, in round numbers, about sixty-four degrees. Consequently, at the moment of firing the visual radius applied to the moon will describe, with the vertical line of the place, an angle of sixty-four degrees.
These are our answers to the questions proposed to the Observatory of Cambridge by the members of the Gun Club:
To sum up--
1st. The cannon ought to be planted in a country situated between 0@ and 28@ of N. or S. lat.
2nd. It ought to be pointed directly toward the zenith of the place.
3rd. The projectile ought to be propelled with an initial velocity of 12,000 yards per second.
4th. It ought to be discharged at 10hrs. 46m. 40sec. of the 1st of December of the ensuing year.
5th. It will meet the moon four days after its discharge, precisely at midnight on the 4th of December, at the moment of its transit across the zenith.
The members of the Gun Club ought, therefore, without delay, to commence the works necessary for such an experiment, and to be prepared to set to work at the moment determined upon; for, if they should suffer this 4th of December to go by, they will not find the moon again under the same conditions of perigee and of zenith until eighteen years and eleven days afterward.
The staff of the Cambridge Observatory place themselves entirely at their disposal in respect of all questions of theoretical astronomy; and herewith add their congratulations to those of all the rest of America.
For the Astronomical Staff, J. M. BELFAST, Director of the Observatory of Cambridge.
