12 Fishery Board for Scotland. 



whole object of our iuquiry. liut we may sacrifice one dimension of 

 space or another, say latitude or longitude ; and we then get that 

 diagram of Temperature contoured against Time and Linear Distance, 

 which we are in the habit of speaking of as an " isopleth " diagram. 

 All of these various types of diagrams are very simple, and all are 

 now in frequent use. 



Besides such diagrams as these, which all deal with actual 

 Temperatures, it is at times very useful to employ another series 

 which represent Anomalies, or differences of temperature, as com- 

 pared with some standard mean. This most instructive method of 

 indicating climatic abnormalities was introduced, some sixty years 

 ago, by the great German meteorologist Dove.* For instance, (rf) 

 instead of showing the actual temperatures, say, in the month of 

 January, along some particular meridian or parallel of latitude, or 

 some other line or route across the sea, it is often instructive to 

 represent these same data in the form of differences from the mean 

 temperature of the year, as this mean temperature in turn varies 

 from point to point. Or, in like manner (e), instead of showing the 

 mean temperature of the sea as it varies along some meridian, say 

 that of 5° E. in the North Sea, it may be extremely instructive to 

 represent the same data in the form of differences from the corre- 

 sponding phenomena along some other meridian, say in the open 

 ocean. Some use of these methods will be made in the following 

 pages. 



Lastly, in dealing with the periodic phenomena of the year, it is 

 of the highest utility to deal with them according to the methods of 

 elementary Harmonic Analysis, as I have more than once explained 

 in previous Eeports. The temperature changes which follow the 

 seasons at any one particular spot are of the nature of a vMve, or 

 sine-curve ; and this w^ave is characterised by three features, or 

 numerical " constants." It is a fluctuation about a certain Mean 

 Temperature, and this phenomenon we have already, so far, con- 

 sidered. Secondly, the fluctuation or " wave " has a certain " ampli- 

 tude," or regular amount of rise and fall. This we shall usually deal 

 with in the form of the " half-range " ; that is to say, not the whole 

 amplitude of the wave, but the average rise from the mean to the 

 summer maximum, or the average fall from the mean to the winter 

 minimum : and we shall find that this phenomenon of Eange or 

 Amplitude often varies according to locality after a very different 

 fashion from the variations in mean temperature. Again, the 

 seasonal wave of temperature has a definite relation to Time, a 

 definite epoch (on the average) at which the maximum and minimum 

 are reached and the fall or rise begins. This date, corresponding to 

 the so-called " phase " of the sine-curve, will also be found to vary 

 from place to place according to its own proper laws. 



This method " of substituting the separate consideration of 

 separate terms of the complex harmonic function for the examination 

 of the whole variation unanalysed " was first employed by Lord 

 Kelvin, in one of his early papers.f 



* The Distribution of Heat over the Surface of the Glohe. London, 1853. 



t "Oil the Reduction of Observations of Underground Temperature ; with Aiiiilication 

 to Professor Foibes's Edinburgh Observations, and the Continued Calton Hill Series," 

 by Professor William Thomson, Trans. R.S.E., xxii. pp. 405-439, 1860. 



