The general appearance of the instrument is well shown in the figure, which is engraved from a photograph I took of Mr. Ekholm while actually engaged in talking through a telephone to M. Hagström as to what portion of a cloud should be observed. The latticework tube, the cross wires in place of an object glass, and the vertical circle are very obvious, while the horizontal circle is so much end on that it can scarcely be recognized except by the tangent screw which is seen near the lower telephone.
Two such instruments are placed at the opposite extremities of a suitable base. The new base at Upsala has a length of 4,272 feet; the old one was about half the length. The result of the change has been that the mean error of a single determination of the highest clouds has been reduced from 9 to a little more than 3 per cent. of the actual height. At the same time the difficulty of identifying a particular spot on a low cloud is considerably increased. A wire is laid between the two ends of the base, and each observer is provided with two telephones—one for speaking, the other for listening. When an observation is to be taken, the conversation goes on 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 formulæ 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.
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 formulæ which are necessarily complicated, and even by using logarithms of addition and subtraction and one or two subsidiary tables—such as for log. sin²(θ/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.
It might have been thought that there would be less chance of mistaking the point of the cloud to be measured, if you had the pictures from the two ends of the base to look at leisurely than if you could only converse through a telephone with the observer at the other end of the base. But in practice it is not so. No one who has not seen such cloud photographs can realize the difficulty of identifying any point of a low cloud when seen from two stations half a mile or a whole mile apart, and for other reasons, which we will give presently, the form of a cloud is not so well defined in a photograph as it is to the naked eye.
At Kew an extremely ingenious sort of projector has been devised, which gives graphically the required height of a cloud from two simultaneous photographs at opposite ends of the same base, but it is evident that this method is capable of none of the refinements which have been applied to the Upsala measures, and that the rate of vertical ascent or descent of a cloud could hardly be determined by this method. But there is a far greater defect in the photographic method, which at present no skill can surmount.