TKANSACTIOKS OF SECTION A. 459 



3. On determining ilte Heights and Distances of Clvuds hy their reflexions in 

 a luw pool of icater, and in a mercurial horir-on. Bij Francis Galton, 

 M.A., F.B.S. 



The calm surface of a slieet of water may lie made to serve the purpose of a 

 huge mirror in a gigantic vertical range-finder, whereby a sufficiently large 

 parallax may he obtained for the efii?ctive measurement of clouds. The observation 

 of the heights and thicknesses of the different strata of clouds, and of their rates of 

 movement, is at the present time perhaps the most promising, as it is the least 

 explored branch of meteorology. As there are comparatively few places in 

 England where the two conditions are found of a pool of water well screened 

 from wind, and of a station situated many feet in height above it, the author hopes 

 by the publication of this memoir to induce some qualified persons who have 

 access to favourable stations, to interest themselves in the subject, and to make 

 observations. 



The necessary angles may be obtained with a sextant and mercurial horizon, 

 but it is convenient, for reasons shortlj' to be explained, to have in addition a 

 tripod stand, with a bar of wood across its top to support the mercurial trough, 

 and some simple instrument for the rapid and rough measurement of altitudes. I 

 have used the little pocket instrument sold by Casella, of ITolboru Bars, London, 

 called a ' pocket alt-azimuth,' and have employed Captain George's mercurial 

 horizon on account of its steadiness and ease in manipulation. 



The observer has to determine : — 



1. The difference of level in feet between the mercury and the pool of water 

 (call it d). 



2. The angle between the reflexions of a part of a cloud in the mercury and in 

 the pool (call it ^7). This should be carefully measured. 



3. The angle between the portion of the cloud and its reflexion in the mercury 

 (call it 2 a). This may be roughly measured ; its altitude a may most conveniently 

 be taken at once by the pocket alt-azimuth or other instrument. The subjoined 

 tables will then give the required result with great ease. 



If ^j be not greater than .3°, and if n be the ntimber of minutes of a degree in ji, 

 the error occasioned by writing n sin 1' for sin n', will never exceed six inches iu a 

 thousand feet, and may be disregarded. Other errors of similar unimportance, 

 due to the eye not being close to the merctiry, may also be ignored. Under these 

 conditions, since log. sin. 1' = 6'4G373, it can be easily shown that 



distance of cloud = - X 6875-5 cos (a + j>). 

 n 



vertical height of cloud = distance x sin a. 



The following table has been calculated for these values when - = 1 . To use 



n 

 it, multiply the tabular numbers by d (the difference in feet between the level of 

 the mercury and that of the pool) and divide by n (the number of minutes of a 

 degree in the angle between the reflexion in the mercury and that in the pool). 

 The result will be the distance, or height, as required in feet. 



Table for calculating distances and height of clouds by their reflexions from a 

 mercurial horizon, and from a pool of water at a lower "level. 



a = Altitude of cloud, (being half the sextant angle between the cloud and its 



reflexion as seen in the mercury, not pool). 

 p = Angle between the reflexion of the cloud in the mercury and that in the 



pool. 

 d - A'ertical height of mercury above pool. 

 n = Number of minutes of a degree in the angle jy. 



Then the distances and heijrhts of clouds = tabular numbers x - 



