July 28, 1892] 



NA TURE 



293 



The next question is, what multiples of these units we should 

 take to make the practical units. In accordance with your 

 request I give my ideas on the subject, premising, however, that 

 I think there is no finality in things of this sort. 



First, if we let the rational practical units be the same mul- 

 tiples of the " absolute " rational units as the present practical 

 units are oi their absolute progenitors, then we would have (if we 

 adopt the centimetre, gramme, and second, and the convention 

 that ^= I in ether) 



[Rr] X 10" = new ohm = x- times old. 

 [Lr] X 10'' = new mac = -i" ,, ,, 

 [Sr] X 10"" = new farad = x'- ,, ,, 

 [Cr] X 10"' — new amp = x~^ ,, ,, 

 [V,-] X 10^ - new volt = x ,, ,, 

 lo? ergs = new joule = old joule. 

 10" ergs per sec — new watt = old watt. 



I do not, however, think it at all desirable that the new units 

 should follow on the same rules as the old, and consider that the 

 /ollowjng system is preferable : — 



[L,.] 



10* = new ohm = "^ x old ohm. 

 10 



10'* = new mac ~ x old mac. 

 10 



[Sr] X lo""* = new farad 

 [C] X 1 



old farad. 



new amp = x old amp. 



[Vr] X lo^* = new volt = .v x old volt. 

 10* ergs = new joule = lo x old joule, 



lo"* ergs per sec. = new watt = lo x old watt. 



It will be observed that this set of practical units makes the 

 ■ohm, mac, amp, volt, and the unit of elastance, or reciprocal of 

 permittance, all larger than the old ones, but not greatly larger, 

 the multiplier varying loughly from \\ to 3 J. 



What, however, I attach particular importance to is the use 

 of one power of 10 only, viz. 10^, in passing from the absolute to 

 the practical units ; instead of, as in the common system, no 

 less than four powers, 10*, 10^, lo**, and 10^. I regard this 

 peculiarity of the common system as a needless and (in my ex- 

 perience) very vexatious complication. In the lo** system I 

 have described, this is done away with, and still the practical 

 electrical units keep pace fairly with the old ones. The 

 multiplication of the old joule and watt by 10 is, of course, a 

 necessary accompaniment. I do not see any objection to the 

 change. Though not important, it seftms rather an improve- 

 ment. (But transformations of units are so treacherous, that I 

 should wish the whole of the above to be narrowly scrutinized.) 



It is suggested to make 10" the multiplier throughout, and the 

 results are : — 



[Rr] X 10" = new ohm = x- x old ohm. 

 [Lr] X 10" = new mac = x' x old mac. 

 [S,] X lO"" =; new farad = x"" x old farad. 

 10 



[Cr] 



new amp 



old amp. 



[V*"] X io» = new volt = \ox x old volt. 



\c? ergs = new joule = 10- x old joule. 



10^ ergs p. sec. — new watt = 10- x old watt. 



But I think this system makes the ohm inconveniently big, 

 and has some other objections. But I do not want to dogmatize 

 in these matters of detail. Two things I would emphasize : — 

 First, rationalize the units. Next, employ a single multiplier, 

 as, for example, lo^. 



Oliver Heaviside. 



P.S. — Heaven preserve us from dynamics based on the Act of 

 Parliament ! 



Neutral Point in the Pendulum. 



In the theory of the pendulum the position of the neutral 

 point of support is a matter of practical importance, which is, 

 nevertheless, quite disregarded. 



Taking a rigid uniform bar as the simplest case, there are 



NO. I I 87, VOL. 46] 



four points of support from which its vibrations are equal, the 

 two ends and the two respective centres of oscillation. But 

 there are t«o >ymmetric points, situated between either end and 

 the centre of oscillation nearest to that end, from which points 

 of suspension the rate of vibration is most rapid. Hence, when 

 suspended from these points, a change in the position of the 

 point of siippoit produces a minimum difference in the rate of 

 vibration. Or, in practical terms, there is a great advantage in 

 having a small amount of overhead weight above the support, 

 as then, if the support approach the bob (owing to changes in 

 elasticity of the spring, or of the knife edges), and so increase 

 the number of vibrations, it recedes from the top weight, and 

 so diminishes the vibrations to a corresponding amount, and 

 vice versa. 



This neutral point of support seems to have been overlooked 

 in the main pendulum researches, as it was what had to be 

 avoided rather than sought in the determination of the length, 

 which was then the main interest. Probably some one has 

 already noticed such an elementary property ; but it is of so 

 much value in minimizing sources of error that it is worth some 

 attention. 



Bromley, Kent. W. M. Flinders Petrie. 



Induction and Deduction. 



Can we determine the precise relation between Induction and 

 Deduction? Both are said to be a species of Inference. De- 

 duction is, no doubt, Mediate Inference. Is Induction Mediate 

 or Immediate Inference ? If Immediate it must be of the form : 



This X is Y (or these X's are Y's) (i) 



.'. All X's are Y's (2) 



But such "inference" as this is not illative; (i) can 

 furnish only a suggestion, not by any means a justification, 

 of (2). 



Still it is true that if, e.g. I have proved that the angles at the 

 base of an isosceles triangle are equal to each other, I hence- 

 forth believe and assert unhesitatingly, that a// isosceles triangles 

 have the angles at the base equal. Hoiv do I justify such a 

 conclusion of an universal from a particular ? In this way, I 

 think : — Every nameable or cogitable object is an identity in 

 diversity — that is, it is itself, it is something, and it has a plurality 

 of characteristics. This principle is involved in the assertion of 

 any statement of the form A is B, and it seems moreover to be, in 

 itself, evident on reflection. Further (as Bacon surmised), every 

 property (or group of properties) has a " form," some invariable 

 and inevitable coexistent. In other words, there is uniformity 

 of coexistence as well as of causation in nature. In the case of 

 any one isosceles triangle, I have seen the connection of interde- 

 pendence that there is between the characteristics of "having 

 equal sides," and "having the angles at the base equal ;" I have 

 perceived it to be self-evident that the one property involves the 

 other. Hence, my whole argument might run thus : — 



Every characteristic is invariably accompanied by some other 

 characteristic ; 



Equality of sides in a triangle is a characteristic ; 



.•. Equality of sides in a triangle is invariably accompanied 

 by some other characteristic. 



Again : — 



Equality of angles at the base is a characteristic which is (self- 

 evidently) inseparable from equality of sides in one [this 

 particular] case ; 



What is in-eparable from equality of sides in one case is in- 

 separable in all cases ; 



.•. Equality of angles at the base is inseparable from equality 

 of sides in all cases — 



That is, all isosceles triangles have the angles at the base 

 equal. 



What we rely on here is Interdependence of characteristics 

 and Uniformity of that interdependence ; i.e. we rely on a 

 principle of coexistence or coinherence, parallel to Mill's "Law 

 of Causation " ; and this is a principle which we find to be a 

 necessary condition of what we accept as strictly self-evident 

 propositions. The assertion with which we conclude in the 

 above generalization, is an assertion of uniformity of inter- 

 dependence between certain specified characteristics. 



Again, if I administer a certain amount of arsenic to a healthy 

 animal, and it dies, and I hence conclude that arsenic is a cause 



