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XLV. On the Physical Cause of Ocean-currents. 

 By William B. Carpenter, M.D., LL.D., F.R.S. 



To the Editors of the Philosophical Magazine and Journal. 



University of London, Burlington House, W. 

 Gentlemen, April 22, 1874. 



MR. J. CROLL, in a note to his last paper (i On the Phy- 

 sical Cause of Ocean-currents ' (Phil. Mag. for March, 

 p. 176), charges me with the following inaccuracy : — 



"Dr. Carpenter states that 48 miles per day is the mean 

 annual rate of the Gulf-stream in the 'Narrows;' but in the 

 Admiralty's Current-chart, published October 1872, the mini- 

 mum rate is stated to be 32, and the maximum rate 120 nau- 

 tical miles per day. This gives 87 statute miles per day, or 

 fully 3| miles per hour, as the mean rate." 



Not being a Statistician, as Mr. Croll professes to be, I should 

 have never thought of deducing a mean rate from a maximum 

 and minimum only, having always supposed that a correct ave- 

 rage could only be based upon a large number Gf data, the 

 larger the better. Thus, if I wanted to know the average number 

 of children of one marriage, I should not take the arithmetical 

 mean between a maximum of (say) 20, and a minimum of 0, which 

 would give 10; but should collect 1000, 10,000, or 100,000 

 observations, and find the mean of the whole. 



This last is precisely what the Meteorological Department, on 

 whose guidance I have relied in this matter, have done in regard 

 to the rate of the Gulf-stream. If Mr. Croll will look into their 

 " Currents and Surface-Temperature of the North Atlantic %x 

 (1872), he will find the following passage (p. 23) under the 

 head of " Remarks on the General Current Chart, constructed 

 from the whole of the observations on the currents employed in 

 this discussion, irrespective of the time of the year in which 

 they were made." 



" The main part of the stream is forced into the Straits of 

 Florida, turning to the N.E. by E., in its passage between the 

 Florida Reefs and Cuba, at a mean rate of 39 miles. About 

 lat. 25° N. the straits between Florida and the Bahamas Bank 

 become contracted, part being known as the Narrows. Here 

 the set becomes almost due N., and its rate greater, averaging 

 48 miles. This rate and set is maintained to lat. 30° N." 



If, again, Mr. Croll will look into the General Chart itself, 

 he will find the first of these averages to be based on thirty- 

 eight observations, the second on fifty-four observations, ani 

 the third on forty observations. 



Or, if he will examine the Monthly Charts, he will find that 

 while six of them give a monthly average below 48 miles per 

 day, there is only one that gives an average so high as 73'6 miles 

 a day. The average of the six months of least rapid rate is 34 



