570 EEPORT — 1903. 



might be left to his own conscience, if he bad one. I doubt if ever a Cambridge 

 mathematician could work either quaternions or vector products blindly. This, in 

 addition to its simplicity, is a great advantage in either sort of vector method. 



But mathematical writers forget that readers are not specialists in their par- 

 ticular branches ; and if an author has a new notation, or unfamiliar conventions, 

 the reader simply cannot hotlier with it. People do not read books ; they dip in 

 and abstract the particular bits of information they want, and if they come across 

 new conventions, or notation, they cannot read the whole book to find out what is 

 meant. Mathematical writers, among their other numerous faults, generally omit 

 to index, and bury definitions in the letterpress, so that they cannot be found except 

 by reading the book from the beginning. They also forget that their readers do 

 not spend their whole time at mathematics, and do not keep the subject in a state 

 of bright polish. An ordinary man, who may be reading physics one hour, and 

 specifying for sewage pumps or interviewing a town council the next, cannot keep 

 his head clear about the idiosyncrasies of diflerent writers ; they are inessential, and 

 are a nuisance. 



If Professor Henrici can induce a committee of influential mathematicians, 

 and especially physicists, to discuss the matter and settle what system to adopt, 

 and stick to it, we may get rid of .r, y, and s, and gain simplicity ; but as long as 

 there is continual tinkering there is no chance of the adoption of any system. It 

 would be better to adopt the worst system than go on as at present. It is for 

 specialists, not for people like me, to say what is wanted. I may put in a plea as 

 a possible though ignorant user. I have no religious objection to the square of a 

 vector being negative. Being an engineer, an ordinary screw is right-handed or 

 positive ; and for mathematicians there is the corkscrew. I want a system that 

 fits in with the electric and magnetic circuits, and I want it to make geometrical 

 sense of \f — \, Demoivre's theorem, and the exponential values of the Irigonometric 

 functions and the hyperbolic functions. We do not want several sets of conven- 

 tions to cover all these points. I do not speak personally, merely as an outsider 

 representing, probably, many hundreds of physicists. We all want some system — 

 one system, and only one system. 



7. Consideration of some Points in the Design and Worki^ig of 

 Ballistic Galvanometers. By P. H. Powell, B.Sc. 



The D'Arsonval type of galvanometer is at the same time one of the most 

 accurate and one of the simplest of galvanometers, and is exceptionally suitable 

 for use in the neighbourhood of powerful electromagnets. 



A ballistic galvanometer is usually designed to have a certain periodic time 

 and a certain sensibility ; it should be quick-working — i.e. should be able to be 

 brought to rest quickly at zero after the deflection has been read. 



The deflection of the galvanometer is a measure of the quantity of electricity 

 discharged through the instrument. It is assumed that the discharge takes place 

 before the suspended coil of the instrument has appreciably moved ; consequently 

 the periodic time must depend upon the time during which the discharge passes, 

 and can be fixed accordingly. Hence the two data, sensibility and periodic time, 

 can be easily chosen, the remaining condition being left for further consideration. 



Consider a coil whose length is a, breadth b, mass M, wound with n turns of 

 wire, and suspended between the poles of a permanent magnet which creates a 

 uniform field of intensity H. 



Then, after the impulse has been given, 



Mi^^'rr -G6, 

 neglecting damping (where C is the control), and hence 



Time of free oscillation T = 27r a/-— , , , • C^) 



