1847.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



3C1 



The remaining subjects of instruction are eminentlj- practical, and need no 

 warning of this kind. 



Quitting for a inoment any reference to tlie especial nature of the subjects 

 taught, there arc two errors diametrically opposed to one another, but to- 

 wards one or other of which almost every person is occasionally tempted. 

 These are idleness and over-exertion. It would be difficult to determine 

 which of the two has been more fatal to the progress of the student. I need 

 hardly tell you how much danger there is in giving way to the idea that 

 when the immediate task is learned, idleness is permissible. In the scliool- 

 boy, indeed, we excuse this, because in most cases the mental effort requires 

 to be succeeded by physical exertion; but for you there can be no such feel- 

 ing. You must advance steadily, constantly, and incessantly, if you would 

 attain that distinction and success which ought to be the object of your 

 ambition. Relaxation no doubt is necessary, but your relaxation must not 

 be idleness. 



On the other hand, you will be tempted in your competition for the 

 honours and prizes offered as the rewards of exertion, to pursue your studies 

 with an unreasonable and excessive ardour, without regard to prudence and 

 health. Tliis is no less an evil than the opposite vice of sloth. You are no 

 inore justified in excess of this kind and in the indulgence of mental excite- 

 ment, than you would be in the unreasonable indulgence of any other pas- 

 sion. Nor can you really benelit by this kind of intemperance. A steady 

 and unwavering progress is most valuable, and tnost permanently useful; and 

 you had far better fail in obtaining tlie prize than obtain it at the cost of 

 health. 



And now that you have been informed of the nature and extent of the 

 education here ali'orded — what we offer you, and what we expect from you — 

 my task, that of introducing you to your work, is for the present at an end. 

 I have mysvlf no fear as to the resnU in your cases individually ; and what- 

 ever may have been or may be the toil and the anxiety of tliose who have 

 superintended the growth of this department of the Applied Sciences, of wliich 

 you are now membeis, — whatever struggles and difficulties we may have had 

 in carrying out our views, with reference to the subject of general scientific 

 education, — however slowly it may have taken root, and however it may have 

 been checked by the apathy of those nbuse other occupations were too pres- 

 ing to allow them to do justice to this, — we are all, I think, satisfied now that 

 as a system it is established ; and that we who liave laiioured earnestly in 

 the cause may fairly expect to see tlie result in our days — although one of 

 those to whom the system owes much, and who would have rejoiced to see 

 its present success, lias unhappily been removed from bis sphere of useful- 

 ness before success dawned upon us. I cannot forbear here this allusion to 

 our late lamented Professor of Chemistry,* for I feel that without his exer- 

 tions we should not this day have been able thus to offer congratulation, as 

 well as to express hope ; and he would, I repeat, have been amongst those 

 most rejoiced could he have seen his views thus far carried into successful 

 operation. 



* Professor Daniell. 



REVIEWS. 



Mathematical Physics; or the Matht.matical Principles of N'atural 

 Philosophy : with a development of the caust.s of Henl, Gdseons Elas- 

 ticity, Gravitation, and other great phemmena of Ndture. By JoH.v 

 Herapath, Esq. London : Whittaker and Co., 1847. 2 vols, royal 

 octavo. 



It is not long since that a Mr. Isaac Frost prochiimed, trump et- 

 mouthed, a discovery of tilt! most stup n lous importance — viz., that 

 the Newtonian Theory was .is untrue as it was blasphemous; that the 

 san was nut the centre of our system, but revolved round the earth at 

 the distance of about 20,000 miles ; that the moon was a block of ice, 

 distant 0,000 miles ; an. I, ".is to the Itngth of the diatmter of the uni- 

 verse, if any gentleman were to ask me that question," says Mr. Frost, 

 " I should answer — ' It is as long as Goo pleases.' " 



Mr. Frost's objections to the theory of gravitation were certainly 

 very plausible. "Newton," observes that astute pliilo>opher, 

 "accounted for the force which drives the earth up the ascending 

 node of the ecliptic, but does not account for the force which rolls it 

 down the descending node;" and again, "if tlie stars are infinitely 

 distant, how is it that tlieir light does not Interfere to produce dark- 

 ness?" This latter objection we consider especially profound, — an 

 opinion which we the more confidently express for two reasons — first, 

 because we entertain it in common with one of the most popular 

 journals of the day; and secondly, because we can't understand it — a 

 sullicient proof with most people of the profundity of an idea. 



About the same time that the unscientific public was astonished by 

 the theories of Mr. Isaac Frost — in opposition to Sir Isaac Newton — 

 the scientific public was gratified by the discovery of a new plan-'t, 

 upon which nu telescope had yet beea turned— ou which no eye had 



ever gated ; which, too remote and obscure to be apprehended by the 

 faculties of sense, was reached by a gr isp of intellect not unwoilhy of 

 him who first interpreted the laws wliicli made necessary the exist- 

 ence of that distant world. How rich must have been the reward of 

 its silent and nnoblrusivp discoverer ! How intense his scorn of the 

 pedants who surrounded him.' With wh it quiet mirth would he turn 

 from their sesqitipedalia verba, their " heini hcxalctrahedrons" and jar- 

 gon, to those cherished results of his toil, the final completion of his 

 Principia! Day, in all her Indian magnificence, had for him less 

 glory than the Nlglil; for Night held tlie treasure he had staked 

 years of thought to win. Mighty w.is his ambition — mightier his 

 success. 



Somewhere in the wide gap between these two great philosophers 

 we would rank Mr. Herapath, — and injustice to that gentleman, be it 

 observed, nearer to Mr. John Couch Ad.nns than to Mr. Isaac Frost. 

 If our author had succeeded in accomplishing all that the lengthy 

 title-p;:ge of his work professes, we should consider him by far the 

 greatest man of his age : profession, however, is not practice, and 

 although we admit tliat some of the theories he has developed are 

 extremely ingenious and supported by a great deal of beautiful rea- 

 soning, yet we confess we are not disposed to accede to the truth of 

 any one of them — simply because they explain only a few, and seem 

 to us quite irreconcilable with the greater number, of the phenomena 

 of nature. 



The cause which Mr. Herapath assigns for heat, gravilation, and 

 the other molecul.ir forces of the universe, is a verv simple one — the 

 assumed hardness and iueitia of the molecules of matter; and the 

 subject of our present review professes to be a general treatise on the 

 action of forces, whether finite or molecul/.r. The first part — on the 

 action and laws of finite forces — is nothing more than a jumbled com- 

 pilation of certain statical and dynamical propositions. Moreover, 

 although the results of these propositions, wliich are all old acquaint- 

 ances (such as to find the centre of gravity, centre of percussion, and 

 the like,) are correct enough, the means by which these results are 

 arrived at are verv questionable, and to lis in most instances wholly 

 unintelligible. Mr. Herapath has adopted the very common error of 

 assuming the fundamental laws of motion to be axiomatic; — no fact 

 can be axiomatic which the mind can conceive to be otherwise than it 

 is : but it is very easy to conceive the laws of motion to be different 

 from what they ready are; therefore the laws of motion are not axi- 

 omatic, and consequently depend on experiment and induction. In 

 the theory of collision, Mr. Herapath is at least original:— having 

 previously admitted that a perfectly hard body, such as he defines it, 

 has never been the subject of experience, and moreover that other 

 bodies, usuallv termed hard, with which we are acquainted, such as 

 iron, granite, &c., are as distinct from perfectly hard bodies as rest is 

 distinct from motion, he proceeds to argue on what would happen 

 supposing two perfectly hard bodies to impinge on each other. He 

 asserts that under such circumstances, the two bodies would each 

 retrace their paths, with velocities equal but contrary to those which 

 they possessed previously to impact. We do not attempt to disprove 

 Mr. Herapath's assertion, but in lawyer style we set up a counter-plea 

 or assertion of our own : we assertthat two "perfectly hard" bodies, 

 after impact, would polka together "for an hour by Shrewsbury 

 clock," and then turn green, — aud we defy Mr. Herapath to disprove 

 o;^r assertion. 



To view the subject more seriously, the phenomena which take 

 place during the impact of two ordinary bodies may be well illus- 

 trated by the following problem:— Suppose two balls, with masses A 

 and B, to impinge directly on opposite ends of a spiral spring, the 

 mass of the spring being neglected in comparison with either of the 

 masses A or B. 



Suppose a were the original length of the spring, z its length at 

 time I from commencement of impact, x the space one end has passed 

 over at time t. Then, since the mass of the spring is indefinitely 

 small, the forces tending to compress it at both ends are equal. Let 

 T be this force at time <;— then we have for the motion of A 

 (i^ _ -T_ 

 dl' — A' 



for the motion of B 



d' (X -{■ z) 



ur 



dx 

 dl 



■f 



T 



b' 



■X.dl 

 A 



Let !* be the velocity A had at first, then c — u. .'. the velocity 

 of A continually decreases, and at time i is diininishel by a quaatity 



/"Xdt p^dt 

 ; and the velocity of B continually dimii.i»lies by / — — 



VI 



