TRANSACTIONS OF SECTION A. 791 



11. Hydrometers of Total Immersion. Bij A. W. Warrington, M.Sc, 



The writer lias made a series of experiments witli the object of showing that 

 the hydrometer becomes an instrument of scientific precision if it is modified so 

 that when used it is totally immersed in the liquid. 



Small ring-shaped platinum weights are slipped over the ungraduated neck of 

 a glass hydrometer until the latter has nearly attained the specific gravity of the 

 liquid to be tested. The temperature of the liquid is then slowly altered until 

 the hydrometer and the liquid have exactly the same specific gravity. 



With proper precautions this method gives results accurate to one in a million 

 for temperatures from 0° to 40° C. 



To determine the specific gravity of a solid a glass hydrometer is employed, 

 which, in form, is not unlike a Nicholson hydrometer without its tray. Two ex- 

 periments are made at approximately the same temperature, in one of which the 

 hydrometer is weighted only with mercurj', and in the other it is weighted with 

 the solid together with the necessary amount of mercury. The results are correct 

 to one in a hundred thousand. 



SATURDAY, SEPTEMBER 10. 



The Section was divided into two Departments. 



The following Reports and Papers were read : — 



Department I. — Mathematics. 



1. Report on Tables of certain Mathematical Functions. 

 See Reports, p. 145. 



2. The Mathematical Representation of Statistics. 

 By Professor F. Y, Edgeworth. 



1. Among methods of representing statistics of frequency Professor Karl 

 Pearson's separation of a given group into two normal curves comes first. This 

 method is based on a vera causa ; such composite groups are known to exist. An 

 accurate fit, too, is obtained. 



2. These advantages attach also to another method, which consists of a second 

 —as the normal law, of a^^'s^— approximation to the result of numerous inde- 

 pendent agencies co-operating. A given unsymmetrical group may commonly be 

 generated by shifting each element of a certain normal curve to a distance which 

 is the square of its original distance from a certain point. This method has two 

 additional advantages : (a) It is easily worked, as the constants can be determined 

 hy percentiles (without taking moments) ; (b) the correlation between unsymme- 

 trical observations may be obtained from the correlation of the generating normal 

 surface. 



3. A third class comprises formulae of which the a priori basis is doubtful. 

 An extreme instance — which, however, fits observations very well— is the juxta- 

 position, with a common greatest ordinate, of the halves of two different normal 

 curves. Formula3 of the third class, obtained by substituting other functions for 

 the square in the second method, are found to fairly represent statistics wholly 

 unsymmetrical, as those of incomes, house valuations, &c. 



3. On the Use of Logarithmic Co-ordinates. By J. H. Vincent. 

 See Reports, p. 159. 



