somewhat as follows:  First observer, who takes the lead—­“Do you see a patch of cloud away down west?” “Yes.”  “Can you make out a well-marked point on the leading edge?” “Yes.”  “Well, then; now.”  At this signal both observers put down their telephones, which have hitherto engaged both their hands, begin to count fifteen seconds, and adjust their instruments to the point of cloud agreed on.  At the fifteenth second they stop, read the various arcs, and the operation is complete.

But when the angles have been measured the height has to be calculated, and also the horizontal and vertical velocities of the cloud by combining the position and height at two successive measurements at a short interval.  There are already well-known trigonometrical formulae for calculating all these elements, if all the observations are good; but at Upsala they do far more.  Not only are the observations first controlled by forming an equation to express the condition that the two lines of sight from either end of the base should meet in a point, if the angles have been correctly measured and all bad sets rejected; but the mean errors of the rectangular co-ordinates are calculated by the method of least squares.

[Illustration:  N. EKHOLM MEASURING CLOUDS.

   This figure shows the peculiar ocular part of the altazimuth,
   with the vertical and horizontal circles.  It also shows the
   telephonic arrangement.]

The whole of the calculations are combined into a series of formulae which are necessarily complicated, and even by using logarithms of addition and subtraction and one or two subsidiary tables—­such as for log. sin squared([theta]/2) specially constructed for this work—­the computation of each set of observations takes about twenty minutes.

Before we describe the principal results that have been attained, it may be well to compare this with the other methods which have been used to determine the height of clouds.  A great deal of time and skill and money have been spent at Kew in trying to perfect the photographic method of measuring the height of clouds.  Very elaborate cloud cameras, or photo-nephoscopes, have been constructed, by means of which photographs of a cloud were taken simultaneously from both ends of a suitable base.  The altitude and azimuth of the center of the plate were read off by the graduated circles which were attached to the cameras; and the angular measurements of any point of cloud on the picture were calculated by proper measurements from the known center of the photographic plate.  When all this is done, the result ought to be the same as if the altitude and azimuth of the point of the cloud had been taken directly by an ordinary angle measuring instrument.