RECENT ADVANCES IN SCIENCE 369 



what complicated intrinsic equation ; the family includes 

 numerous well-known curves, notably Ribancour's curve and 

 the sinusoidal spiral. 



A. R. Forsyth, Messenger, xlviii (1919), pp. 131-144, dis- 

 cusses the consequences of assuming various laws of facility of 

 error. 



A. Guldberg, Comptes Rendus, 168 (1919), pp. 815-817, 

 examines Bravais' law of error ; Bravais established the law 

 for spaces of three and four dimensions, but was unable to 

 extend it ; but Guldberg shows that, by his methods, the 

 law can be at once extended to w-dimensional space. 



T. J. I'A. Bromwich, Phil. Mag., (6), xxxviii (1919), pp. 

 23 1—235, gives some formulae, derived from Stirling's formula, 

 which have applications to Bernoulli's theorem in the theory 

 of probability. 



J. W. L. Glaisher, Quarterly Journal, xlviii. (191 8), pp. 151- 

 192, publishes the first of a series of papers on early tables of 

 logarithms and the early history of logarithms. The main 

 topics of this paper are Napier's logarithms and the transition 

 from them to decimal logarithms. Dr. Glaisher emphasises 

 in his introduction the inadequacy and incorrectness of exist- 

 ing accounts. 



G. H. Bryan, Math. Gazette, ix(i9i9), pp. 333-352, gives 

 very compact four-figure logarithm tables, including logarithm 

 tables of the trigonometric functions to every two minutes. 

 The tables are free from repetitions frequent in most tables, 

 and are in that respect superior when space is a consideration ; 

 when space is not a consideration the repetitions possibly 

 save mental effort when large masses of computations have to 

 be performed. 



W. W. Johnson, Messenger, xlviii (1919), pp. 145-153, gives 

 an historical account of Napier's ' circular parts ' of spherical 

 triangles. 



ASTRONOMY. By H. Spencer Jones, M.A., B.Sc, The Royal Ob- 

 servatory, Greenwich. 



The Total Solar Eclipse of 191 9, May 28-29. — During the past 

 two years frequent reference has been made in Science Pro- 

 gress, in these notes and elsewhere, to Einstein's generalised 

 theory of relativity. An essential feature of this theory is 

 the so-called " principle of equivalence " according to which 

 a gravitational field is indistinguishable from a spurious field 

 of force produced by an acceleration of the axes of reference. 

 Einstein showed that the theory was capable of accounting 

 exactly for the so-called anomaly in the motion of the peri- 



