Let us return to our instrument.  We have traced upon a diagram the distance of the points of attachment of the thread, at the intersection of the planes of projection.  We have thus obtained the position of the line, N S. Then, operating as has just been said, we have marked the point, P. Now, accurately measuring all the angles, we have found:  N S R = 50 deg.; P H H¹ = 18 deg.; P E E¹ = 65 deg..  The first shows that the instrument has been constructed for a place on the parallel of 50 deg., and the others show that, at the solstices, the height of the sun was respectively 18 deg. and 65 deg., decompounded as follows: 

  18 deg. = polar height of the place -231/2 deg..
  65 deg. = " " " " +231/2 deg..

The polar height of the place where the object was to be observed would therefore be 411/2 deg., that is to say, its latitude would be 481/2 deg..

Minor views of construction and measurement and the deformations that the instrument has undergone sufficiently explain the divergence of 11/2 deg. between the two results, which comprise between them the latitude of Paris.

After doing all the reasoning that we have just given at length, we have finally found the means by which the hypothetic bead was to be put in place.  A little beyond the curves, a very small but perfectly conspicuous dot is engraved—­the intersection of two lines of construction that it was doubtless desired to efface, but the scarcely visible trace of which subsists.  Upon measuring with the compasses the distance between the insertion of the thread and this dot, we find exactly the distance, N P, of our diagram.  Therefore there is no doubt that this dot served as a datum point.  The existence of the bead upon the thread and the use of it as a rude calendar therefore appears to be certain.

The compass is to furnish us new indications.  After dismounting it—­an operation that the quite primitive enchasing of the face plate renders very easy—­we took a copy of it, which we measured with care.  The arrow forms with the line O C-O R an angle of 90 deg. + 8 deg..  The compass was therefore constructed in view of an eastern declination of 8 deg..

Now, here is what we know with most certainty as to the magnetic declination of Paris at the epoch in question: 

Years.  Declinations. 1550. 8 deg. east. 1580. 11.30 1622. 6.30 1634. 4.16

On causing the curve (Fig. 3, No. 3) to pass through the four points thus determined, we find, for 1612, the declination 81/2 deg..  This is, with an approximation closer than that of the measurements that can be made upon the small compass, the value that we found.  From these data as a whole we draw the two following conclusions:  (1) The instrument was constructed at Paris; and (2) the inventor was accurately posted in the science of his time.

Certain easily perceived retouchings, moreover, show that this sun dial is not a copy, but rather an original.  We are therefore in an attitude to claim, as we did at the outset, that the constructor of this pleasing object was not only an artist, but a man of science as well.