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.
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. 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.
We saw that the altazimuth employed at Upsala had no lenses. The meaning of this will be obvious to anyone who looks through an opera glass at a faint cloud. He will probably see nothing for want of contrast, and if anything of the nature of a telescope is employed, only well-defined cloud outlines can be seen at all. The same loss of light and contrast occurs with a photographic lens, and many clouds that can be seen in the sky are invisible on the ground glass of the camera. Cirrus and cirro-stratus - the very clouds we want most to observe - are always thin and indefined as regards their form and contrast against the rest of the sky, so that this defect of the method is the more unfortunate.
But even when the image of a cloud is visible on the focusing glass, it does not follow that any image will be seen in the picture. In practice, thin, high white clouds against a blue sky can rarely be taken at all, or only under exceptional circumstances of illumination. The reason seems to be that there is very little light reflected at all from a thin wisp of cirrus, and what there is must pass through an atmosphere always more or less charged with floating particles of ice or water, besides earthy dust of all kinds. The light which is scattered and diffused by all these small particles is also concentrated on the sensitive plate by the lens, and the resulting negative shows a uniform dark surface for the sky without any trace of the cloud. What image there might have been is buried in photographic fog.
In order to compare the two methods of measuring clouds, I went out one day last December at Upsala with Messrs. Ekholm and Hagström when they were measuring the height of some clouds. It was a dull afternoon, a low foggy stratus was driving rapidly across the sky at a low level, and through the general misty gloom of a northern winter day we could just make out some striated stripes of strato-cirrus - low cirro-stratus - between the openings in the lower cloud layer. The camera and lens that I use habitually for photographing cloud forms - not their angular height - was planted a few feet from the altazimuth with which M. Ekholm was observing, and while he was measuring the necessary angles I took a picture of the clouds. As might have been expected under the circumstances, the low dark cloud came out quite well, but there was not the faintest trace of the strato-cirrus on the negative. MM. Ekholm and Hagström, however, succeeded in measuring both layers of cloud, and found that the low stratus was floating at an altitude of about 2,000 feet high, while the upper strato-cirrus was driving from S. 57° W. at an altitude of 19,653 feet, with a horizontal velocity of 81 and a downward velocity of 7.2 feet per second.