_ 3 — D'AKCY W.'llIOMRSÜN 



WC can speak with great confidence, inasmuch as we have consecutive information re- 

 garding them, month by month, for several consecutive years : others of which we have 

 much useful knowledge, but marred here and there by gaps: and again there are other 

 areas for which our statistics are but fragmentary and must be used with great circums- 

 pection. 



It is important to consider, especially in cases where our information is imperfect 

 and fragmentary, how far we shall be justified in throwing together into a single average 

 the results of several separate years: for to do this is apparently, if not obviously, con- 

 venient, in order to get (for instance) a single general view of the seasonal fluctuations. 

 To answer the question fully we should have to enter somewhat deeply into the theory 

 of statistics, but it must suffice to point out now that the method has its dangers as 

 well as its advantages. If the results of the several years are in fair agreement one with 

 another, a combination of them all will display more clearly the common underlying 

 truth. But, on the other hand, if there be essential differences between one year and 

 another, then the composite result may be such as never actually occurs. Suppose, for 

 instance, that a large migration of fish takes place into a certain area once a year, but 

 that in one year this migration happens to take place a few months earlier than in 

 another; then if we combine, without further question, the results for these two years, 

 we shall apparently have evidence (which is of course incorrect) of a double migration 

 at two separate seasons of the year. Many other and similar instances might easily be 

 furnished of the fallacies into which too hasty combination or "slumping" of our results 

 may easily lead us. The lesson to be learned is twofold: firstly, that we must not draw 

 deductions from composite averages without scrutinising them in the light of the indi- 

 vidual numbers on which they are based, this scrutiny being all the more obligatory the 

 fewer the individual numbers are; secondly, that we must distinguish with as much care 

 as possible between the values of our several results, some of which are, as it were, 

 "nails in a sure place", while others are of the nature of surmises, resting on insuffi- 

 cient proof It follows from all this that a full and complete discussion of our statistics, 

 even in the case of a single fish, would be a very lengthy matter. In this paper only 

 the main results are brought together, as briefly as possible, and a certain number of 

 curves are shown in illustration of some of the most important or best ascertained facts. 



Our information is most copious and least subject to interruption in respect to the 

 areas off' the east coast of Scotland (XXIII, XXIX), around the Pentland Firth (XVII) 

 and eastward thereof (XVIII, XIX), and around Shetland (X): it is somewhat less 

 abundant from the north-west of Scotland (C, D), from Orkney eastward across the 

 North Sea (XIII, XIV, XV, XVI), eastward from Aberdeen over the Witch Ground 

 (XXIV, XXV) and also from the Faeroe and Iceland fishing-grounds. From one or other 

 area, to the north, east and south of those just mentioned, we have in some cases a 

 good deal of information regarding particular facts, or particular periods but not enough 

 to give us a clear and convincing picture of the whole course of the fishery. 



The chart of the North Sea, is divided, according to Dr. Fulton's method, into 

 forty-eight squares (see PI. II, fig. 2 for the numbers of the areas), numbered consecutively, 

 each square corresponding to 2 ° in latitude and i ° in longitude, the western boundary 

 at first selected being the meridian of 4° W. There is nowadays a great fishing to the 

 westward of this boundary, especially at Rona and Sule Skerry. Hence it has been ne- 



