372 



KNOWLEDGE. 



September, 1910. 



idea of motion, augmentation), not a statical concept. Tliis 

 (last) affords an instance of 'the incommensurable' achieved, 

 represented (say) by an infinite straight line, or by the infini- 

 tude of space (when regarded as something already present) 

 which exemplifies a statical concept : since Space does not 

 augment, while Time does. 



Sir W. Hamilton and Mansel ((juoted in Spencer's First 

 Prmciplt's) object to any classification of Infinites among 

 themselves : this implying, as they say, " plurality " of the 

 Infinite. This is seen in the following passage, viz. : — 



'■ How self-destructive is the assumption of two or more 

 Infinites is manifest on remembering that such Infinites, 

 by limiting each other, would become finite." (First 

 Principles, p. 811. 



But let us take the statical concept of space traversed by 

 an imaginary straight line. We then observe that, harmonising 

 with incommensurability, viewed towards the right the line 

 is infinite in length, also, viewed towards the left the same 

 can be asserted. But it is evident that these two " Infinites," 

 by limiting each other, do not " become finite." 



A prismatic column of space of (say imagined! square, or of 

 any shaped (finite) transverse section, great or small, prolonged 

 through space (entirely) would evidently, as to contents, 

 enclose an infinite volume. And any number''' of such 

 universes (infinite in cubic content) could exist without mutual 

 encroachments of territory, and e\eu with lateral intervals of 

 imagined unoccupied space, relati\ely narrow or \\'ide between 

 them. 



In the instance of infinite pcist Time (in one sense a statical 

 infinitude as remarked), that species of contradiction or "anti- 

 nomy,' peculiar to certain transcendental ideas, may be, at the 

 outset, suspected. And here we have an infinitude [of time] 

 already elapsed, whereas it is predicated of infinitude that it is 

 ne\er to elapse. And how is that to elapse which is not even 

 to be begun ? 



A correlated ■ antinomy ' in the instance of infinite /)(?;n-t' 

 Time, is by no means so easy to see ; this essay having, so far, 

 failed to discover any, and I am not aware if one has been 

 definitely formulated. 



The following consideration seems however to point to an 

 antinomy in this case also, which might be suspected before- 

 hand, from correlation with infinite past Time. 



In regard to the coming future, some cjuantity (let us call it 

 chronographic length) nnist be virtually transferred over, and 

 located inside the point C. i.e., between C and A. If no more 

 tha.n a. " finite" quautiiy or length be transferred inside the 

 point C, the procedure (i.e., the lapse of time) will come to an 

 end. Accordingly the length AC (notwithstanding the first 

 argument) cannot " remain " finite, and nuist consequentiallv 

 become more than finite. 



But since we ahx-ady recognised the inconcei\ability of 

 setting a limit to the conservation of a Finite [AC] by a 

 process of gradual (i.e., non-catastrophic) addition effected ; 

 therefore by such uniform rate of addition, the (elapsed) length 

 AC must surely remain finite, however great it become. Hut 

 we saw that by an opposing argument, apparently rivalling 

 the first in its validity, the length AC must become more than 

 finite. Hence antinomy discovered accordingly. 



Some, however, might consider it a chief condition to cite 

 the fact (say for illustration merely) that in order to parallel 

 infinite future Time, an infinite supply of material for our 

 ideal chronographic registering-strip would be required. But 

 there is a noteworthy distinction between an inconceivability 

 and an antinomy (or an antithesis in logic). For while the 

 first constitutes something negative and indefinite, the second 

 constitutes something positive and definite. 



Still, it may be answered — The presentation of antinomies 

 is not unusual by Infinitudes ; but the fact may not necessarily 

 invalidate their existence. A demonstration, one way or the 

 other, may be difficult to furnish, and, whatever may be the 

 true view here, one is at liberty to search and to point out 



what the antinomies are, indeed this procedure constitutes a 

 needful and proper accompaniment to progress. 

 Yours faithfully, 

 S. TOLUER PRESTON, Ph.D. 

 Klein Flottbek, bei Altona, 

 Germany. 

 April-June. 19W. 



CONVENIENT SEATS FOR SMALL TELESCOPES. 

 To the Editors of " Kxowledge." 



Sirs, — The delightful little picture sent by Mr. Thomas; 

 which was reproduced in the April number of " Knowledge,' 

 and his praise of an apple-case as a convenient seat, provokes 

 me to utter a word of advice to the owners of small telescopes. 



There are two accessories to the instrument, the absence of 

 which will render it practically useless. This is a tall stand 

 and a convenient seat. Mr. Thomas's stand looks as if it were 

 just perfect for that small glass, but I demur to his " seat." I 

 feel quite sure that the right way to use a small telescope is 

 to sit down first and then to draw the legs of the stand 

 towards you and around you till the eye-piece comes to the 

 eye ; the eye should not be put up to the eye-piece but the 

 instrument brought to the eye. A deck chair answers well, 

 and the final adjustment is to push a big handkerchief or some 

 such cushion in behind the head till the eye or eye-piece are 

 properly related. If the observer is in a strained position he 

 is terribly handicapped, f he attitude of that young observer 

 is as hopelessly unpractical as it is perfectly charming. 

 Yours faithfully. 



J. A. HARDCASTLE. 



THE MOON AND THE WEATHER. 

 To the Editors of " Knowledge." 



Sirs, — Having read Mr. Strickland's article in JuK- number' 

 may I be allowed to follow in his footsteps ? 



Here, one hundred and fifty miles from the mouth of the 

 p'raser River, and on its left bank, with us the wind decides 

 the weather, and often the tides control the winds, and, as is 

 accepted, the moon governs the tides. 



The tides are not felt further up the Eraser than to the 

 mouth of the Harrison River, yet the inrush of warm water 

 causes, as an effect, a warming up of the atmosphere farther east. 



Now I have in my nffice a record of the weather for 1905, 

 6, 7, and 9 ; 8 I missed. And in my memory records of many 

 other years for the time of the full moons between December 

 21st and January 3rd, and the tides with this full moon are 

 inxariably extremely high all along the North Pacific coast, so 

 that before Vancouver became a city, and man was somewhat 

 primitive, the boat houses, boats and wharves suffered consider- 

 able damage. Now these tides cause a warming-up of the 

 atmosphere and consequent displacement of cold, which is 

 felt far inland. Whether the effect is the same Ea.st of the 

 Rocky Mountains I cannot say, not having given any attention 

 to the weather there. So noticeable is the effect along the 

 banks of the Eraser, that what is known as a ground thaw 

 is seen, that is, the ground being covered with ice. the ice 

 becomes loose from the ground beneath it becoming soft from 

 the warm current of air. 



The weather means much to us, as we farm a large acreage 

 and have to feed stock in winter, and we have to keep an eye 

 on it, and to assist in a forecast we look overhead to observe 

 the wind currents, which in this clear, bright part of the world 

 can be seen pushing and fighting, cornering and dodging, and 

 thrusting for the mastery — a battle of the clouds — and then 

 we go to the almanac to see how the moon is, and v\-ork 

 accordingly, taking things easy or rushing to get the hay or 

 grain in, cattle housed, and so on. 



GEORGE DITCHAM. 



St. George's Industrial School 

 For Indian Boys, 



Lytton, B.C. 



The (finite) breadth of ti;uisverse section of any oite of such space-prisms of imagined infinite lengtli, eacli capa)dt; uf comprising a cosmos, 

 might even be supposed comparable (say) to the estimated breadth of our (visible! stellar universe, or, of course, greater, if we like. 

 Speculative llioughl, maintained uithin the range .if the possible, may occasionally conduce to raise fresb questions 



