44 



NA TURE 



[May 9, 1907 



German coast. We easily see the extent of difference in 

 seasonal range of temperature, which near our own coast 

 runs from less than 6° C. to more than 13° C, at 2° east 



5c25 St24 Sc23 



from less than 6° C. to more than 15° C, and off the 

 Get man coast from less than 4° C. to more than 17° C. 

 We notice next how comparatively slow are the changes of 

 temperature when near the minimum in winter and the 

 maximum in summer, and how rapid in spring and autumn 

 when near the middle of the rise and fall, and we also per- 

 ceive that the fall takes place somewhat slower than the 

 rise, for the isopleths are less crowded in autumn than in 

 spring. Lastly, we may discern that lines joining the cusps 

 of the closed curves, in other words, the lines of minimum 

 and maximum, tend to run somewhat obliquely across the 

 chart, and that the maximum at least is definitely later 

 as we appi'oach the Continental coasts. Similar charts for 

 various other routes show essentially the same pheno- 

 menon, and those drawn from the Scottish coast in the 

 direction of Norway tend to show the influence of land at 

 both ends of the route, the range of temperature being 

 least in the middle. 



Similar diagrams may be drawn for any given depth, 

 and Fig. 2 is so drawn for a depth of 100 metres on a 

 line from Buchan Deep, near Aberdeen, to the Viking 

 Bank between Shetland and Norway. In this diagram we 

 see that as we leave the coast the temperature-isoplelhs 

 diminish rapidly in number, until in the neighbourhood 

 of our station xxiii. (about 59° 40' N., 0° 40' E.) the 

 seasonal change is only from something loss to some- 

 thing more than 7° ; but as we go further north we come 

 again to a region of larger temperature variations, where 

 the maximum is considerably higher and the minimum not 

 quite so low. \\'e notice also a retardation of dates, the 

 maximum not being attained until well on in September. 



Another series of diagrams, of a kind that has been 

 more frequently employed, and notably by Dr. H. R. Mill 

 in his work on the Clyde sea area, shows temperature 

 plotted by means of isopleths over coordinates represent- 

 ing time and depth. While the former diagrams showed 

 temperature changes along a line of stations during 

 successive months, but for one depth only, these diagrams 

 show the changes at all depths during successive months, 

 but at one point of space only. 



These and other methods of representing sea tempera- 

 tures by means of diagrams may be supplemented by the 

 use of empirical formulx. The rise and fall of surface 

 temperature at a given point is a very simple wave that 



can be suitably expressed as a sine-curve. In the periodic 

 temperature-function 



/(e) = A„-(-A, sin (»-!-(;, )-l-Aj sin (29-(-Cj), 

 Src., 6 is an angle increasing in proportion to the lime, 

 A„, A,, Aj arc constants expressed in degrees centigrade, 

 and e is a phase angle of which each degree signifies 

 approximately one day in advance or arrear of our starting 

 point, namely (since we are dealing with monthly means), 

 January 15. If we submit an annual series of tempera- 

 ture observations to harmonic analysis, we find that the 

 first sine-factor differs but little from the actual curve, 

 while the third and following factors are entirely negligible. 

 If we deal with mean temperatures at a given point over 

 several years, we find the simple sine-formulae still more 

 closely applicable. Thus, for the surface temperatures atj 

 Abertay, taking the mean of ten years, 1803-1903, \vi 

 obtain the formula /(S) = S-43 — 4.32 sin ((*-f 60°), and fini 

 that results calculated from this formula for the middl 

 points of the successive months differ in no case by so 

 much as half a degree centigrade, and by a mean differ- 

 ence of only one-fifth of a degree centigrade, from the 

 means of the observed temperatures for the said months. 

 If we were to apply the next factor of our harmonic 

 formula [-f-o.29 sin (26-1-49°)] "^ should obtain calcu 

 lated results showing a maximum discrepancy 

 observation of about a quarter of a degree, and a meai 

 discrepancy of one-tenth of a degree. 



After repeated trials of this kind we come to the con- 

 clusion that the sine-formula is a safe representation of 

 the annual wave of temperature change. That it is a 

 highly convenient one is obvious, for, in the first place, it 

 gives us at a glance the three essential factors of the 

 phenomenon, the mean temperature (A„), the range or 

 half-range of temperature (.^1), and the phase (e,), which 

 last we may briefly describe as the mean retardation of 

 maximum and minimum. Furthermore, it enables us to 

 compare these three factors very easily for a series of 

 adjacent stations or for successive years. Thus if we work 

 out our formula for points a degree of longitude apart on 

 the route from Leith to Hamburg we obtain a table of 

 which the following is a part : — 



Tah\e 0/ Harmonic Constants for Surface Temperatures. 

 Leith to Hamburg. 



iqo4 1005 



Long. Ao Ai ci A,, .^i a 



i 



m^t 

 ^ 



This orderlv succession of constants may then anew be 

 transferred to diagrams, as in Fig. 3. Similar data may 



also be transferred to charts, of which a series is printed 

 in the report. 



Lastly, if it be granted that a sine-curve approximately 



NO. 1958, VOL. 76] 



