10 DR HUGH ROBERT MILL ON THE 



to appeal directly to the eye, the sections were coloured in accordance with the principle 

 that the merging of one temperature into another should be represented by the 

 corresponding merging of shades or colours. The coldest water was represented in 

 purple, and at intervals of 2° dark-blue, light-blue, blue-green, green, yellow-green, 

 yellow, orange, and deepening shades of red were employed, so that the increasing 

 warmth of the colour corresponded in the order of the spectrum with the increasing 

 warmth of the water. All the sections were drawn on paper ruled in millimetre 

 squares, and by counting the number of squares between successive pairs of isotherms 

 the mean temperature of the whole section was readily calculated. 



In the case of a loch, however, the really interesting datum to secure is the mean 

 temperature at a given time of the whole mass of water, and this was arrived at by 

 the following method: — The mean temperature of each zone of 10 or 15 fathoms was 

 ascertained by the process of counting squares" between the isotherms crossing the zone, 

 and the figure so secured was multiplied by a factor which took account of the mass 

 of water in that zone. Thus the 10 fathoms of water next the surface spreads over a 

 much greater mean superficial area than the next horizontal slice of 10 fathoms, and 

 the lowest zone of ten fathoms has a very small mean area indeed. Thus, if fig. 1 

 (Plate XXII.) be an average transverse section of a loch, the mean temperatures of 

 successive zones of 10 fathoms of which have been ascertained in the longitudinal 

 section, and the lines a, b, c, &c, being the length of the side of the rectangle, having 

 the same area as the section cut off between successive depths of 10 fathoms, the 

 mean temperature M of the whole loch would be represented by 



-««- _ m x a + m 2 6+m 3 c-|-m^+. . . 

 a+b + c+d + . . . 



where m v m 2 , &c, are the successive mean temperatues of the longitudinal zones of 10 

 fathoms. This assumes that the isothermal surfaces are horizontal, which is not strictly 

 true. From the few cases of observations which allowed of the construction of transverse 

 sections showing isotherms, it appears that the isothermal surfaces are normally slightly 

 arched in the centre, and when disturbed by transverse winds they are tilted up on one 

 side nearly to the same degree as they are tilted down on the other, thus leaving the 

 mean thermal condition identical with that expressed by isothermal surfaces drawn 

 horizontally through the central soundings. In calculating thermal changes, all data 

 are referred to half tide, as it was found impossible, from the observations available, to 

 distinguish tidal disturbances from the other periodic phenomena. In the case of the 

 Channel and Great Plateau, which may be looked on as bodies of water of practically 

 uniform thickness throughout, the average temperature of the mass is given sufficiently 

 closely by the average of the mean temperatures of the various vertical curves. 



Another very instructive method of discussion of vertical distribution of temperature 

 is to construct diagrams showing thermal change in depth and time at some particular 

 station. Time is marked as abscissae, depth as ordinates, and the isotherms of each 



