Mar. 5, 1874J 



iNATURE 



543 



series shall we select for our graduations ? Equal fractions of its 

 length will never do — I mean such as one-tenth, two-tenths, &c. 

 — because of tlie great inequality of the variation in diffeicnt 

 parts of the series, being insensible between those whose position 

 is near its middle and great between those at either end. I pro- 

 pose to use a scale founded on tlie law of Frequency of Error, 

 which gives a scale of equal parts wherever that law applies, 

 and I use the " probable error" for the unit of the scale. Thus, 

 in a row of a hundred individuals the graduations of + 2", + i", 

 0°, — 1°, — 2°, resjiectively would be at the following places, in 

 percentages of the length of the series : — 2, 9, 25, 50, 75, 91, 

 9S. We know that {he law of Frequency of Error applies very 

 closely to the linear measurements of the human form. Now 

 suppose that I want to get the average height and " probable 

 error" of a crowd of savages. Measuring them individually is out 

 of the question ; but it is not difficult to range them — roughly for 

 the most part, but more carefully near the middle and one of the 

 quarter points of the series. Then I pick out two men, and two 

 only — the one as near the middle as may be, and the other near 

 the quarter point, and I measure them at leisure. The height of 

 the first Iran is tlie average of the whole series, and the difference 

 between him and the other man gives the probable error. The 

 question I put is, whether any more convenient subdivision of a 

 series can be suggested for mtnvrsa/ use than that above men- 

 tioned. Its merits are, that it applies very fitly to linear mea- 

 surements of all natural groups ; also to errors of observation, 

 which arc akin to many of the moral qualities, for the 

 measurement of which the scale is especially needed. It 

 would not apply to weight, but is less out of relation to it 

 than most persons might think, because weig '.Is do not vary as 

 the cubes of the heights. Tall men are often thin, and short 

 ones are fat, and the curious fact seems thoroughly verified that 

 the general relation between height and weight is strictly as the 

 sijuarcs. {.See Gould's " Sanitary Memoirs of the War of the 

 Rebellion," Cambridge, U.S., 1869, p. 408 — 410.) If we arrange 

 a series and graduate it according to equaldifferencesof the squares 

 of the heights of the men, we are not so far astray as if we had 

 dealt with the cubes. But I cannot imagine any quality, unless 

 possibly music and memory, to vary so rapidly towards tlie large 

 end of the series as the latter division would show. To sum up : 

 subdivision in equal parts is of no use practically, and is there- 

 fore out of the question ; the law of error will do very accu- 

 rately for many large groups of cases ; the law of error modi- 

 fied by being brought into relation to bulk will rarely, if ever, 

 be right for other qualities. It therefore seems to me reasonable 

 to adopt the law of error series, as the best compromise, and to 

 accept it as " the common statistical scale." If, for example, 

 I estim.ite a soldier's energy at + 2° (S.S.), I state what every- 

 body who cared to inquire into the subject would construe in 

 exactly the same sense as I used the phiase, and he would also 

 be inclined to believe, until better informed, that the difference 

 between such a man's energy and that of a man of -Y 0° (S.S.) 

 was twice as great as between him and a man of -t- i^ {S.S.). 



Lastly, liow can we best find individuals who represent the 

 o', ± i", c&c. , of any and every quality, that they may be studied 

 and their abilities illustrated and described, so as to serve as per- 

 manent standards of reference ? These would gradually give us 

 means of finding the equivalent of the S.S. graduation in the 

 natural scale — as we might learn to say, -V 4' (S.S.) of energy 

 = + 3°'5 in the natural scale. Those who have to deal with 

 bodies of men, whether as examiners, instructors, masters, over- 

 seers, or officers, could best tell. How about the ordinary sub- 

 jects of competitive examination ? Is there any optical observation 

 made under (sensibly) identical circumstances and with (.sensibly) 

 identical instruments, of which the probable error of each ob- 

 server is known ? If one could only get two or three hundred 

 nautical observers together, and make them take sextant 

 angles of the same objects, and learn the probable errors 

 of each, we should have data to give us once for all the 

 values of the S.S. as regards ability to observe, in terms of 

 absohiie values. Can no drawing-master give accurate de- 

 scriptions of the delicacy of touch of his pupils, con'espond- 

 ing to the graduations of the S.S. scale ? How about mechanical 

 manipulation among operatives ? How about music and memory? 

 Each separate quality requires and deserves a monograph, which, 

 once thoroughly well done, would become a most valuable stan- 

 dard of comparison and check upon the S.S. scale, which it must 

 be remembered is securely based on no ground except that of 

 statistical constancy, but which, when it proves to bte a scale of 

 equal parts, is doubly acceptable. 



I will not go on writing now, being rather desirous of raising 

 discussion and learning more, than of saying all my say. 

 42, Rutland Ga'e, S.W. Francis Galton 



Simultaneous Meteorological Observations 

 With reference to the scheme of international simultaneous 

 observations prop .sed by the War Department of the United 

 States and adopted by the Meteorological Congress at Vienna in 

 .September las'-, a provis'onal arrangement was entered into at 

 Vienna, between General Myer and myself, at his desire, by 

 which the Scottish Meteorological Society was to assist the 

 American Government in carrying out the proposed scheme by 

 an exchange of meteorological observations between the two 

 bodies. At a meeting of the Council of this Society on 

 February 9, a letter was read from General Myer, dated January 

 27, 1874, formally requesting the co-operation of this Society in 

 carrying out the international scheme, which letter being iden- 

 tical with the one on the same subject published in Nature 

 (vol. ix. p. 300). it is unnecessary to subjoin. 



A considerable number of observers have been already ob- 

 tained in connection with the scheme, and copies of the Ameri- 

 can Monthly Weather Rt-'ie-ii and Daily Meteot olo^ical Record 

 have, along wiih the special schedules for the observations, been 

 sent to them, as an acknowledgment on the part of the Ameri- 

 can Government for their assistance in the work. The Council 

 are ready to receive the assistance of others of their own ob- 

 servers, and of any other observers who may be willing to co- 

 operate in this cosmopolitan scheme, from which cosmopolitan 

 benefits may be confidently looked for. 



Alexander Buchan 

 Scottish Meteorological Society, Edinburgh, March 2 



The Limits of the Gulf-stream 



Much discussion has recently taken place respecting the limits 

 of the Gulf-stream, and the Admiralty Chart of the North At- 

 lantic, published last year, is supposed to embody all that is 

 known of its boundaries. My observations, however, which have 

 extended over a series of years, differ so widely from it that I am 

 induced to send you an abstract chart of them. 



In December 1S72 I found the stream wedged in to a distance 

 of fifteen miles off Cape Hatteras, and following the coast-line at 

 that distance to Roanoke Sound. On arriving in Norfolk I 

 found that the reports of several ships corroborated my observa- 

 tions. 



The remarkable bend east of George's Shoals is confirmed by 

 H.M. S. Gannct, and also by the Nantucket fishermen and pilots. 



Maury, in his "Physical Geography of the Sea," makes the 

 stream, in summer, wash the southern shores of Newfoundland, 

 but in no month ol the year have I found it so far north as the 

 red line in the accompanying chart. I am of opinion that if it 

 once passed over the bank every codfish would be destroyed. 

 The highest temperature recorded by me in September on this 

 line is 56°. 



At the points of sudden change I have seen the ripples at the 

 distance of a mile previous to entering them. Those which are 

 recorded may be relied on to a mile, as I have discarded those 

 made from dead reckoning. In every case the deep blue colour 

 of the sea, the presence of sun-fish, Portuguese men-of-war, and 

 numerous debris, confirmed the observations made with the ther- 

 mometer, and I may add, what is of more importance to seamen, 

 the strong easterly set. 



The southern boundary of the s'ream is taken from the observa- 

 tions of five years. As summer advances it becomes more difficult, 

 when east of Bermuda, to detect the line ol demarcation, for the 

 rays of the sun heat the water almost to Gulf-stream temperature 

 right down to the limit of the trade-wind. From the data which 

 I have been able to collect, as well as from personal observation, the 

 limits of icebergs in the Admiralty Chart appear to be equally 

 erroneous. To me it appears impossible that bergs could drift 

 square across the heated waters of the Gull-stream tolat. 39° N. 

 almost in the teeth of the prevailing summer winds, and a strong 

 north-easterly set of two miles per hour. The Admiralty Chart 

 gives the current a higher velocity. 



The most southern iceberg ever seen by a Cunard steamer 

 (and there cannot be a higher authority) was in lat. 43° 10' N., 

 long. 49° 40' W., and the most eastern, which has come under my 

 observation, by the Grace Gibson, on June 11, 186S, which ship 

 passed four between lat, 43''iS N, and43°ao' N.undlong, 4i°aQ' 



