September 9, 1920] 



NATURE 



51 



known physical conditions, with the onset of 

 maturity or even with migrations into different 

 waters, and as such they have enormous value. 



But, after studying the results obtained, certain 

 investigators have doubted the validity of this 

 method of ascertaining growth. It was noticed 

 that in all species so investigated the calculated 

 lengths for the first and succeeding- winters 

 became successively less and less as they were 

 found from older and older fish, and other 

 apparent discrepancies were pointed out by dif- 

 ferent observers. As a matter of fact, the above 

 method gives only a first approx- 

 imation to the actual lengths to 

 which the fish grows at the end 

 of each winter of life. It is based 

 on the assumption that the 

 lengths of the scale are them- 

 selves proportional to the length 

 of the fish — a closer approxima- 

 tion (but still an approximation), 

 for the calculation is given by 

 taking- the increments of growth 

 of the scale as proportional to the 

 increments of growth of the fish, 

 starting from the point at which 

 the scale first appears, which is 

 in most cases aji amount suffi- 

 ciently appreciable tj affect the 

 calculations of the first two or 

 three winter lengths consider- 

 ably. 



In Fig. 3 the average relations 

 in the observed lengths of the 

 scale and the corresponding fish, 

 and in the observed lengths of 

 the fish and the corresponding 



the length at which the scale begins to grow. In 

 the case of North Sea herring c is about 3 cm. 



As in practice only relative lengths of the 

 winter rings are measured on the scale, the 

 constant a in the equation can be eliminated, and 

 the calculated lengths to any previous winter 

 (Lj, Lj, etc.) derived from the equation put in the 

 form 



L,-<:-f^(L-4etc. 

 The results obtained by the use of this formula 



scales, are shown by the dots 

 and crosses respectively. 



A mathematical relation can be found by com- 

 bining all the corresponding measures of scales 

 and fish. This is known as a correlation coeffi- 

 cient, and in the case depicted was very high, viz. 

 r = o-9S. The points lie very nearly on straight 

 lines, known as "regression lines," the mathe- 

 matical equations to which are L = 4-8V-f-3 and 

 V = o-i9L — 0-36. From the first of these equations 

 the length of the fish can be calculated when the 

 length of the scale is known from measurements. 



The general form of this equation for any series 

 of measurements of fish and their scales is 

 L = aV-i-c, the constant term c corresponding to 



S 8 10 iz I* 16 la to it 2* te la io 

 Length oF Herring in Cms . 



Fig. 3. — Showing average^relationM between Rieasutementt offish and their ica1«t. 



approximate more closely to values derived from 

 observation than in the case of the original 

 formula when c is not taken into account, and 

 the growth measures calculated in this way can 

 therefore be assumed to be a closer approxima- 

 tion to the truth. 



In all cases of age and growth determination 

 individual records may be wrong, owing to one 

 or other of many difficulties that may occur in 

 deciphering the scale, but the latest work on the 

 subject has shown that average values, both of 

 ag-e distribution in a sample and of amount of 

 growth, are approximately correct. 



The Structure of the Atom. 

 By C. G. Darwin. 



I. — Atomic Number. 



THE study of the interior structure of the atom 

 was initiated about twenty-five years ago 

 by J. J. Thomson's discovery of the electron. 

 Electrons are particles of negative electricity of 

 charge 477x10-" electrostatic units and mass 

 9-OXIO-" gr., and they were shown to be con- 

 NO. 26«?4. VOL. I06I 



stituents of every type of matter. Some years 

 previously Thomson had shown on theoretical 

 grounds that any charged body should possess 

 extra mass on account of its charge, and these 

 two facts taken together suggested the possi- 

 bility of an electrical theory of matter, whereby 

 all mass should be electromagnetic in origin, and 



