238 



NATURE 



iJan. 3, 1889 



a similar manner the submerged line of growing corals im- 

 mediately outside the weather-edge of the reef of Keeling 

 Atoll would form a barrier-reef, if it was removed some miles 

 from the shore instead of being only about 100 yards distant. 

 As it is now situated, it lies too close to the edge of the present 

 reef to prevent the obliteratioo of the channel inside it after it 

 has reached the surface. Its lagoon channel would be very 

 quickly filled with sand ani x^zi-debris, and as a result we 

 should merely have a permanent addition to the present reef- 

 flat, which, when the process was complete, would be lo.) yards 

 wider. The process is the same as in the case of a barrier-reef, 

 the difference in the result being due to the submerged line of 

 corals being too close to the edge of the reef for the preservation 

 of the interior channel ; and this circumstance is due to the fact 

 of the submarine slope being greater than in the case of a coast 

 fronted by a barrier-reef. These remarks are merely intended 

 to be suggestive. They may, perhaps, direct the attention of 

 of other observers to the examination of the outer slopes of 

 atolls and to their mode of seaward growth. This can only be 

 done during unusually calm weather. 



I have discovered many other new features of minor interest 

 in connection with Keeling Atoll, to which I will refer in my 

 full description of these islands. The island of Noith Keeling, 

 lying fifteen miles to the north, is a small atoll connected wiih 

 Keeling Atoll by a bank. I hope to describe it at some future 

 time. 



In conclusion, I may state that most of my observations 

 in these islands were directed towards estimating the age of 

 Keeling Atoll. These data have yet to le worked up, and 1 

 am fairly confident of getting a satisfactory estimate. The 

 lagoon is rapidly filling up with sand and coral, but it is almost 

 impossible to state in precise terms the changes since the visit of 

 the Beagle, as the survey then made was little more than a sketch. 

 The present Admiralty chart is of but little service in inquiring 

 into past changes, for in it the original survey of the Beagle in 

 1836 has received several later additions, and there is nothing to 

 distinguish the one from the other. For the purpose of navigation, 

 and for the advantage of science, a complete examination of 

 these islands ^hould be made. The best season for surveying is 

 during the calm weather of the months of January and February, 

 when boats can venture close to the edge of the reef, and a 

 satisfactory examination of the outer shores, as well as the 

 interior of the atoll, can then be made. In collecting informa- 

 tion from the residents, it will be necessary to remember that no 

 records are kept in the islands ; and in studying past changes the 

 observer will have to receive what may at first sight appear to be 

 very interesting facts with scientific caution. Some corroboration 

 of such facts should always be looked for. 



Yours faithfully, 



Batavia, November 8. H. B. Guppy. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, December 20, 1888. — " Correlations and their 

 Measurement, chiefly from Anthropometric Data." By Francis 

 Galton, F.R.S. 



Two organs are said to be co-related or correlated , when 

 variations in the one are generally accompanied by varia- 

 tions in the other, in the same direction, while the closeness 

 of the relation differs in different pairs of organs. All varia- 

 tions being due to the aggregate effect of many causes, the 

 correlation is a consequence of a part of those causes having 

 a common influence over both of the variables, and the larger 

 the proportion of the common influences the closer will be 

 the correlation. The length of the cubit is correlated with the 

 stature, because a long cubit usually imi-lies a tall man. If the 

 correlation between them were very close, a very long cubit would 

 usually imply a very tall stature, but if it were not very close, a 

 very long cubit would be on the average associated with only a 

 tall stature, and not a very tall one ; while, if it were nil, a 

 very long cubit would be associated with no especial stature, 

 and therefore, on the average, with mediocrity. The relation 

 between the cubit and the stature will jerve as a specin.en 

 of other correlations. It is expressed in its simplest form 

 when the relation is not measured between their actual 

 lengths, but between (a) the deviation of the length of the 

 cubit from the mean of the lengths of all the cubits under dis- 

 cussion, and {h) the deviation of the mean of the corresponding 



statures from the mean of all the statures under discussion. More- 

 over these deviations should be expressed on the following method 

 in terms of their respective variabilities. In the case of the 

 cubit, all the measures of the left cubit in the group under dis- 

 cussion, and which were recorded in inches, were marshalled in 

 the order of their magnitude, and those of them were noted 

 that occupied the first, second, and third quarterly divisions of 

 the series. Calling these measures Q„ M, and (^.j, the devia- 

 tions were measured from M, in terms of inches divided by 

 ilQa-Qi). which divisor we will call Q. Similarly as regards 

 the statures. [It will be noted that (j is practically the same as 

 the probable error.] This having been done, it was found that, 

 whatever the deviation, y, of the cubit might be, the mean value 

 of the corresponding deviations of siaiure was o'Sj/ ; and, con- 

 versely, whatever the deviation, y' , of the stature might be, the 

 mean value of the corresponding deviations of the cubit was 

 also o'8y. Therefore this factor of 08, which may be ex- 

 pressed by the symbol r, measures the closeness of the correlation, 

 or of the reciprocal relation between the cubit and the stature. 

 The M and Q values of these and other elements were found to 

 be as follow : ' left cubit, i8 05 ando'56 ; stature 67 '2 and i 75 ; 

 head length, 7*62 and O'lg ; head breadth, 6 00 and o'i8 ; left 

 middle finger, 4*54 and 0-15 ; height of right knee, 2050 and 

 o'8o ; all the measures being in inches. The values of r in the 

 following pairs of variab'es were found to be : head length and 

 stature, 0"35 ; left middle finger and stature, 070 ; head breadth 

 and head length, 0*45 ; height of knee and stature, o'g ; left 

 cubit and height of right knee, o"8. The comparison of the 

 observed results with those calculated from the above data 

 showed a very close agreement. The measures were of 350 

 male adults, containing a large proportion of students barely 

 above tweniy-one years of age, made at the laboratory at South 

 Kensington, belonging to the author. 



These results are identical in form with those already arrived 

 at by the author in his memoir on hereditary stature (Proc. Roy. 

 Soc, vol. xl, p. 42, 1886), when discussing the general law of 

 kinship. In that memoir, and in the appendix to it by Mr. J. 

 D. Hamilton Dickson, their rationale is fully discussed. In 

 fact, the family resemblance of kinsmen is nothing more than 

 a special case of correlation. 



The general result of the inquiry was that, when two variables 

 that are severally conformable to the law of frequency of error, 

 are correlated together, the conditions and measure of their 

 closeness of correlation admits of being easily expressed. Let 

 x^, Xj, x„ &c., be the deviations in inches, or other absolute 

 measure, of the several "relatives " of a large number of " sub- 

 jects," each of whom has a deviation, y, and let X be the mean 

 of the values of x^, x.^, x-^, &c. Then (i) y = rX, whatever 

 may be the value of ^. (2) If the deviations are measured, not 

 in inches or other absolute standard, but in units, eac!i equal to 

 the Q (that is, to the probable error) of their respective systems, 

 then r will be the same, whichever of the two correlated variables 

 is taken for the subject. In other words, the relation between 

 them becomes reciprocal ; it is strictly a correlation. (3) r is 

 always less than i. (4) r (which, in the memoir on hereditary 

 stature, was called the ratio of regression) is a measuie of the 

 closeness of correlation. Other points were dwelt upon in the 

 memoir, that are not mentioned here : among these was as fol- 

 lows : (5) The probable error, or Q, of the distribution of x^, 

 x^, X3, &c., about X, is the same for all values oi y, and is equal 

 to sj{^- ^~) when the conditions specified in (2) are observed. 



It should be noted that the use of the Q unit enables the 

 variations of the most diverse qualities to be compared with as 

 much preci>ion as those of the same quality. Thus, variations 

 in lung-capacity which are measured in volume can be compared 

 with those of strength measured by weight lifted, or of swiftness 

 measured in time and distance. It places all variables on a 

 common footing. 



"Preliminary Account of the Morphology of the Sporophyte 

 oi Splacknum Itdetim." By J. R. Vaizey, M.A., of F'eterhoute, 

 Cambridge. Communicated by Francis Darwin, F.R.S. 



' The head length is here the maximum length measured from the notch 

 below the brow. The cubit is measured with the hand prone, from the flexed 

 elbow to the tip of the n.iddle finger. The height of knee is taken from a 

 -■^tool, on whiclt the foot rests with the knee fle.xed at right angles ; from this the 

 measured thickness of the heel of the boot is subtracted. A'l measures had to 

 be made in the ordinary clothing. The smallness of the number of measures, 

 viz. 350, is of little importance, as the results run with fair smoothness. 

 Neither does the fact of most of the persons measured being hardly full grown 

 affect the main results. It somewhat diminishes the values of M, and very 

 slightly increases that of Q, but it cannot be expected to have any sensible 

 influence on the value of r. 



