Bull. — 'hi a Sew Form oj Seismograph. 69 



all be logically connected. Not one, but several, unproved 

 assumptions must be made before a definite geometry can be 

 constructed. The difficulty does not arise from shortcomings in 

 the definitions, though these are undoubtedly defective. Frame 

 what definitions we please, we must still assume certain matters 

 of fact, or alleged matters of fact (call them axioms or call them 

 postulates), before we can logically raise the superstructure of 

 the Euclidian geometry. Even if we define straight lines and 

 planes as such lines and surfaces that the propositions of Euclid 

 respecting straight lines and planes shall be true respecting 

 them, even by this extreme procedure we get no nearer the 

 desired goal : for it then remains to be proved that straight 

 lines, planes, parallels, &c, exist in the space in which we live. To 

 assume that they do is to assume a whole congeries of axioms. 

 A writer named Thomson once wrote a book called " Geometry 

 without Axioms,'' which was certainly a desperate effort to get 

 rid of uuproved assumptions. The attempted proof of the 

 redoubtable 12th axiom was a perfect labyrinth of intricate pro- 

 positions ; but, like all similar efforts, like any efforts which 

 may be hereafter made to ground geometry on definitions and 

 dispense with axioms, it was but " as the helpless waves that 

 break upon the iron rocks of doom." 



The science of the space in which we live is a physical and 

 experimental science, and, unlike arithmetic, algebra, and all the 

 branches of mathematical analysis (the general theory of mani- 

 folds among them), cannot be evolved out of man's inner 

 consciousness. 



Art. VIII. — On a new Form of Seismograph. 

 By F. Bull. 



[Read before the Wellington Philosophical Society, 23rd September, 1885.] 



The prevalence of earthquakes in New Zealand, and at the same 

 time the uncertainty in the reports from the different parts of 

 the colony, as to their occurrence and direction, owing to the 

 want of proper instruments for their detection, led me to con- 

 sider the possibility of devising an apparatus which would at 

 once place on record the occurrence of shakes and indicate their 

 direction. Accordingly I set to work, and commenced by plan- 

 ning all sorts of complicated machines, which did not at all 

 satisfy me ; and I eventually came to the conclusion that the 

 most simple and direct-acting machine wuula be the best for the 

 purpose. 



The first plan I then adopted was to suspend a heavy sphere 

 of lead, having on its under- side a small tube, fixed vertically, 

 in which a pencil fitted, with freedom to ascend and descend in 



