1130 Notices respecting New Books. 



water between two marks on the aspirator gauge (and after- 

 wards for running out a definite volume of water, equal to 

 800 c.c. nearly) , starting from the same initial conditions, 

 was taken with and without the field. 



Assuming the motion to be non-turbulent, which we 

 reasonably can do, the viscosity must vary directly as the 

 time of outflow. In the experiment a potential difference of 

 580 volts between plates *31 mm. apart did not produce a 

 change of even 1 sec. in 9 min. 39 sec. The potential 

 gradient was 18000 volts per cm. nearly, the sparking 

 potential gradient being 31000 volts per cm. 



In setting an upper limit to a possible change in the 

 viscosity due to the electric field, attention must be paid to 

 the " resistance " of the other parts of the channel besides the 

 tube. The time of flow without the field was to the time of 

 flow with it as 4*5 : 10 nearly. The resistance of the tube 

 may therefore be taken to be (10 — 4'5)/10 of the total 

 resistance. The present experiment may therefore be inter- 

 preted to prove the absence of any change in the viscosity of 

 air greater than or equal in amount to *3 per cent. 



I am grateful to Prof. A. W. Porter for his kind interest 

 in the experiment and for his valuable suggestions. 



1st May, 1922. 



OXXI. Notices respecting New Boohs. 



Multilinear Functions of Direction and their uses in differential 

 geometry. By E. H. Neville, late Fellow of Trinity College, 

 Cambridge, Professor of Mathematics in University College, 

 Reading. (Cambridge: At the University Press. 8s.6d.net. 

 1921.) 



IN this small book Prof. Neville has given a systematic discus- 

 sion of functions of several independent directions. In the 

 course of the development of ideas which are to some extent 

 generalizations of the ideas of differential geometry, a number of 

 propositions which actually occur in modern differential geometry- 

 are included. The way in which these theorems are involved in 

 the wider theory which is here introduced, gives an insight into 

 the co-ordinating power of the more comprehensive lines of 

 development which the book describes. 



The exposition is throughout clear and interesting. The sub- 

 ject matter provides one more example of the way in which 

 mathematics covers the domains of abstract thought with ideas 

 of ever increasing generality. 



