April 2,0, 1874J 



NATURE 



499 



Study of Insects," gives a short and popular account of 

 entomology generally, by taking a series of types from 

 amongst the best-known North American insects, and 

 describing them in detail. We should have liked to 

 find some of the descriptions rather more explicit, as they 

 might have been, without any alteration in the size of the 

 volume, if some of the illustrations had not been so fre- 

 quently repeated. In a work like Euclid there is no doubt 

 considerable advantage in having the figures so placed 

 that it is not necessary to turn over the pages in referring 

 to them, especially when it has to be read by boys ; but 

 when space is short and the subject of such general 

 interest, we cannot help feeling that their repetition, three 

 times in more than a single instance, is quite uncalled 

 for. The author's own work at the development of 

 Insecta, which he has published in the " Memoirs of the 

 Peabody Academy of Science," enables him to take a 

 larger view of his subject than that held by most. This 

 is particularly indicated in the very suggestive chapter 

 entitled " Hints on the Ancestry of Insects," in which the 

 researches of Ganin, Lubbock, Brauer, Haeckel, and 

 Miiller are all brought to bear on such questions as the 

 relation of the Zoca form of the embryonic Crustacean to 

 the similarly undeveloped and generalised, here termed 

 Lepius, form of Insecta, in which the configuration is 

 ovate, the head is large, bearing from two to four pairs 

 of mouth-organs resembling legs, and the thorax is 

 merged with the abdomen ; this general embryonic form 

 characterising the larva; of the Arachnida, the Myriapods, 

 and the true Insects. The elaborate observations of the 

 first-named of these authors on the development of 

 Platygaster error, an ichneumon parasite, in the author's 

 mind tend to confirm the theory held by him that the 

 ancestry of all the Insects, including the Arachnids and 

 Myriapods, should be traced directly to the worms. We 

 recommend this small book to all interested in the pro- 

 gress of this branch of invertebrate zoology. 



The Transactions of t]u Academy of Science 0/ St. Louis, 

 vol. iii. No. I. (St. Louis, U.S., 1873.) 



This volume contains a journal of the proceedings of the 

 Society from March 1S6S to January 1873, and a few 

 papers in cxlenso. The latter are : — Notes on the Genus 

 YuLCa, by G. Englemann ; On the new Genus in the 

 Lepidopterous Family Tineid;c, with Remarks on the 

 Fertilisation of the Yucca j and Supplementary Notes on 

 Pronuha yuccasella, by C. V. Riley ; Descriptions of 

 North American Hymciioptera, by B. D. Walsh ; Atmo- 

 spheric Electricity, by Dr. A. Wislizenus, being the yearly 

 report of atmospheric electricity, temperature, and 

 humidity, from observations made at St. Louis ; Cata- 

 logues of Earthquakes for 1871, by R. Hayes ; and On 

 the Occurrence of Iron Ores in Missouri, by J. R. Gage. 

 Mr. Hayes, on the basis of the recorded earthquakes from 

 1739 to 1S42 has found that the "largest maxima 

 occurred in the years of the heliocentric conjunction and 

 opposition of Jupiter and Saturn, with but three excep- 

 tions, and in these cases the increase began in those 

 years, but the maximum was not reached till the follow- 

 ing year." He suggests that " these planets induce 

 electric currents which call into action those forces to 

 which the causes of seismic phenomena are usually 

 ascribed." 



LETTERS TO THE EDITOR 



\Tlie Editor docs not hold himself responsible for of inions expressed 

 by his correspondents. No notice is taken of anonymoui 

 communications. ] 



Herbert Spencer and a priori Axioms 



Mr. Herbert Spencer (vol. ix. p. 461) has "ended what 

 he has to say on the vexed question of the origin of physical 

 axioms " by laying down — 



(i) That "the perceptions and inferences of the physicist 



c.T-njt stand without preconceptions which are the products of 

 simpler experiences than those yielded by consciously-made experi- 

 ments.''^ 



(2) That " the preconception which immediately concerns us 

 is t:ie exact quantitative relation between cause and effect." 



(3) That " if definite quantitative relations between causes and 

 effects be assumed ii priori, the Seco nd Law of Motion is an 

 immediate corollary." 



By speaking of it as an " immediate corollary," I presume that 

 Mr. Spencer means that Newton's Second Law of Motion is the 

 proposition obtained by substituting for the general term, 

 cause, the particular term, force, and for the general term, effect, 

 the particular term, motion i;cnerated ; so that, according to 

 Mr. Spencer, this law simply asserts "a definite quantitative re- 

 lation between a force .and the motion generated by that force." 

 But surely the quantitative relation asserted by Newton is not 

 only definite, but is further the special relation of proportionality ; 

 so that, if the law is an immediate corollary of an it priori as- 

 sumption, the assumption must be that "the exact quantitative 

 relation between cause and effect is that of direct proportionality," 

 or in more familiar words, that " effects are proportional to their 

 causes." Perhaps this is what Mr. Spencer meant to assert. At 

 any rate let us admit it as a definite basis for reasoning, and en- 

 deavour to deduce some consequences from it. 



"The cause of a stone falling when left to itself is its weight ; 

 but ' the greater the cause, the greater the effect,' therefore the 

 greater the weight of the stone the more quickly will it fall, and 

 thus of two stones let fall from the same height, the heavier will 

 reach the ground sooner than the other." Something of this 

 kind, it may be presumed, was the argument of Aristotle and his 

 followers before the age of Galileo : and liow on d priori princi- 

 ples is it to be refuted ? Of course it is disposed of at once by 

 the simple observation that the same force does not produce the 

 same motion in different masses : but independently of some 

 such observation or experiment, it seems to me impossible to 

 deny that it may be true, though even an a priori philosopher 

 might show that, as other alternatives are conceivable, it is not 

 necessarily true. As a matter of historical fact, Galileo refuted 

 it once for all by the " consciousiy-made experiment " of letting 

 two different weights fall simultaneously from the leaning tower 

 of Pisa. 



But it may be said that the above argument is hardly "defi- 

 nitely quantitative." Let us then examine Newton's Second 

 Law of Motion as an "immediate corollary" of our d priori 

 assumption. Here the cause is "the motive force impressed," 

 and the effect " the alteration of motion." But then the question 

 arises — how are the quantities of this cause and effect to be 

 measured? Newton carefully defines quantity of motion as pro- 

 portional to ?nass and velocity ]o\n\.\y ; that is, he measures it by 

 momentum. From another point of view it would have been 

 correct to measure quantity of motion by kinetic energy or vis 

 viva, that is, as proportional to mass and the square of the 

 velocity jointly. Further the " alteration of motion " might be 

 measured either with respect to a given time or to a given space. 

 Newton implies the former, and consequently the explicit state- 

 ment of his second law is that " the momentum generated in a 

 ^/t'i-;/ /mi? by an impressed force is proportional to that force." 

 Substitute for this " the momentum generated in moving through 

 a given space," or " the kinetic f«;';-iy' generated in a given time," 

 and the law becomes untrue. Substitute " the kinetic energy 

 generated in moving through 3. giz'en space," and we have a law 

 which is true, but not that which Newton asserted as his second 

 law. Now among these four alternatives how is our d priori 

 philosopher to decide ? He might perhaps analyse them further 

 and show that some of them are inconsistent with the others, 

 and I believe he might reduce the questions to be decided to 

 still simpler ones ; but I fail to see (in common, I believe, with 

 eviry-;v who has thoroughly grasped the fundamental principles 

 of ra ij .;. mechanics) how, without recourse to consciously-made 

 observations or experiments, he could arrive at a certain conclu- 

 sion. 



May we not say t' en that these great d priori principles, what- 

 ever value they may have in a " System of Philosophy," are of 

 little avail in any special science, and that the "axioms" of such 

 science, however much they may involve these principles, are not 

 mere "immediate corollaries" therefrom? 



If not intruding too much on your space, I am tempted to 

 apply to Mr. Spencer's great principle of the "Persistence of 

 Force " the same mode of treatment as I have applied above to 

 the principle that " effects are proportional to their causes. " 



