August 12, 1920] 



NATURE 



in 



that we are confronted with questions about dis- 

 tances, angles, and so on. We are bound to inter- 

 pret the distance (5) between the points [a + b», 

 c-\-di) and (a' + b'j, c' + d'i) as given by 



and there are corresponding theorems about 

 angles. 



On the whole, we think Prof. Hatton's book 

 will be most useful in suggesting ways in which 

 the Cartesian way of regarding complex points 

 (and lines) is brought into line (without sacrificing 

 logic) with the projective theory. What we may 

 call the complex point (OP), meaning the involu- 

 tion (with a definite sense) of which O is the 

 centre, and -OP2 the invariant (Og.OQ'=: -OP2), 

 is a perfectly definite idea, and is a special case 

 of von Staudt's representation of any complex 

 point in the harmonic form (OooPP') or (OooP'P) 

 with the initial point O. 



Von Staudt's theory is purely projective, apart 

 from the discussion of improper casts. The 

 Cartesian theory is bound to deal with metrical 

 quantities, such as distance and angle, and simply 

 because these notions are derivative, it offers a 

 field of research of a more complicated character. 

 It may be asserted with some confidence that any 

 real extension of von Staudt's theory will be of a 

 metrical kind, and that, if it is worth anything, 

 it will be applicable to three dimensions (or more) 

 as well as to two. G. B. Mathews. 



P. S.— Since the above was written, I have had 

 time to reflect further upon Prof. Hatton's book, 

 and have read Prof. G. H. Hardy's review of it 

 in a recent number of the Mathematical Gazette. 

 I do not wholly agree with Prof. Hardy's attitude, 

 because I still think that there are geometrical 

 notions not reducible to arithmetic — still less to 

 formal logic. But I do agree with him that 

 Prof. Hatton's book has no theoretical value, 

 and, disagreeable as it is, I think it is my duty to 

 say so, especially as I have been informed that 

 another reviewer has praised the book in absurdly 

 exaggerated terms. G. B. M. 



Motion Study and the Manual Worker. 



Motion Study for the Handicapped. By Frank B. 

 Gilbreth and Dr. Lillian Moller Gilbreth. 

 (Efficiency Books.) Pp. xvi+165. (London: 

 George Routledge and Sons, Ltd., 1920.) 

 Price 8s. 6d. net. 



THE work of Mr. Frank B. Gilbreth upon 

 applied motion study and fatigue study is well 

 known, and the present volume describes various 

 extensions and additions to his previously recorded 

 NO. 2650, VOL. 105] • 



methods, especially with the intention of assist- 

 ing men who are handicapped by the loss of a 

 limb or of their eyesight. In Mr. Gilbreth's latest 

 scheme the manual worker whose movements are 

 being studied has a small electric light attached 

 to the hand or other working member of the 

 body, and thereby the path of the motions made 

 can be determined in detail if a series of photo- 

 graphs is taken by kinematograph. Other photo- 

 graphs are taken with a stereoscopic camera, and 

 by this means the path of the motion in three 

 dimensions is ascertained. It is then possible to 

 construct wire models showing exactly the path of 

 a given motion, and such models are found to be 

 very useful for instruction purposes. Series of 

 models are exhibited at the Smithsonian Institu- 

 tion, Washington, and elsewhere, so that skilled 

 mechanics are able to see for themselves what 

 are considered to be the best methods of per- 

 forming certain motions, and to determine if they 

 themselves fall short of the ideal. 



Again, Mr. Gilbreth represents on diagrams, 

 termed "simultaneous-motion cycle charts," the 

 results of his studies on micro-motion. Such charts, 

 when read downwards, present in chronological 

 sequence the various activities performed by any 

 member of the body, the posture taken during 

 the action, and the time consumed. If read 

 across, the charts give a record of all the work- 

 ing members of the body at any one time, and 

 they enable one to see which parts of the body 

 are working most and which are being delayed. 

 It is maintained that this chart system enables 

 the workmen to visualise their efforts graphically, 

 and thereby to lessen waste and increase efficiency. 



The great ingenuity of Mr. Gilbreth's methods 

 will be admitted by everyone, but it is more im- 

 portant for us to determine their practical value. 

 Mr. Gilbreth photographs champions playing base- 

 ball, champion typists, skilled surgeons when 

 operating, in addition to skilled tradesmen, and 

 he believes that the skill shown is in every 

 case based on one common set of fundamental 

 principles, the principles of economy of effort and 

 rhythm of motion. The application of this hypo- 

 thesis to practical ends is, however, very far dis- 

 tant. The concrete instances quoted of the em- 

 ployment of micro-motion study in actual prac- 

 tice are very few and not very striking, but doubt- 

 less it will take a good deal of time before they 

 can be adequately tested and applied. 



The portion of the book devoted specially to the 

 handicapped describes several useful methods, 

 though it strikes the uninitiated that they could 

 have been evolved equally well without elaborate 

 micro-motion study and motion-cycle charts. The 

 one-armed typist is supplied with a typewriter 



