August 22, 1895] 



NA TURE 



405 



Polar. 

 9-85 io"-29 9"-S7 9".46 9"-4i 9"-40 9"-34 



Eijiialorial. 

 9"-67 io"-oS 9"-48 9"-33 io"-03 g'vs 9" -41 

 In relative values 



Polar. 

 10:9 1021 loog 1014 93S 965 993 



Equatorial. 

 1000 1000 1000 1000 1000 1000 lOOO 



At first siglit it wmikl seem that the later August measures do 

 not support the rule. Closer consideration will, however, show- 

 that they do. I'"or while in July the polar cap was still large, 

 and in consequence reached to the limb, even when its centre 

 was at some distance from it, by Augvist it had <lwin<lled to so 

 small a jiatch as to be incapable of doing so when at the same 

 angular distance away. Taking account of this fact, it will be 

 seen that the effect is quite in accordance with the position, as 

 comes out clearly in the relative values for the two diameters of 

 August 14 and August 21. 



It w ill now be evident why so large, and intrinsically so un- 

 mistakable, an effect as that of the Martian twilight should 

 hitherto have escaped detection ; the reason being that the 

 twilight effect and the irradiation from the polar cap each 

 increased their respective diameters to a simultaneous augmenta- 

 tion of both, conspiring each thus tf> mask the other. 



Had measures been continued through a series of months, and 

 been made in sufficient number, both causes must have made 

 themselves evident. Kor both are periodic, and their periods are 

 not the same. The irradiation from the polar cap has a primary 

 period of thirty-seven days, a secondary one of a Martian year 

 as well as a third depending on the tilt of the pole toward the 

 earth ; that of the twilight fringe a varying one of about 

 thirteen months. But as previous measures have been made 

 quite regardless of the twilight effect, and largely regardless of 

 the polar cap, regardless, that is, of its varying position, the 

 results have merely disagreed with each other, and the disagree- 

 ments Ijecn cre<lited to errors of observation. One result of 

 this was discordance in the value of the polar flattening. 



When w'e take both causes into account we find that the 

 means of the July and August observations confirm the October 

 and November ones. 



Kor by comparing the values of the polar diameter when on 

 and away from the limb, it is possible to deduce both the amount 

 of the irradiation from the polar cap and the value of the 

 twilight band from the measures themselves. The results in 

 the case of Mr. Douglass agree with those of his October- 

 November measures. In the case of Prof. Pickering, there is 

 the same relative difference between the determinations, although 

 tlie absolute values are all smaller. 



That in the table the corrections to the July and August 

 measures differ from those applied to the later ones, comes from 

 the dilTerent manner of their taking ; in the July and August 

 measures the limgitudinal thread of the micrometer having been 

 set to the phase axis or perpendicular to it, instead of to the 

 polar one. 



In Mr. Douglass' determinations the value for the twilight arc 

 comes out 8". This is somewhat smaller than the result from 

 the November measures. But a smaller value is jirecisely what 

 should have been found. Kor the greater the phase angle, thi; 

 less the foreshortening, which foreshortening by massing the 

 illumination lets the fringe of light become evident farther out. 

 Now the average phase angle was 43° in July and .August, as 

 against iSi" in November. 



Krom Prof. Pickering's measures the twilight arc comes out 

 greater, or 11", and by inference would have come out greater 

 still in November. 



Thus it appears that measures made by separate observers, and 

 measures made before and after opposition, all confirm each other 

 to the existence of a twilight band upon the jilanet. 



Percival Lowell. 



THE FOUNDATIONS OF ENGINEERING 



EDUCA TION.^ 



T ET us consider what is the education which a young man 



needs to fit him for the jjrofession of engineering, whatever 



be the special line of engineering which he proposes to follow. 



1 Extracted from a course of lectures delivereil in tlie Lowell Institute, 

 Boston, I)y Prof. (i. Lanza, Professor of Theoretical and .Applied Mechanics, 

 Massachusetts Institute of Technology, .and ])ublished in the /ottr/ut/ o( the 

 Franklin Institute. 



NO. 1347, VOL. 52] 



And, before discussing the details of what he ought to study, 

 let us consider what it is that we desire to accomplish by giving 

 him an engineering education. Naturally, we wish, as far as any 

 education can accomplish it, to put him in the best condition to 

 meet and grapple w ith the duties, the probleins, and the respon- 

 sibilities of his profession, as they arise. 



There are two things which are absolutely necessary to make 

 a successful engineer : first, a knowledge of scientific principles 

 and of the experience of the past ; and second, his o» n experience. 

 The last cannot be given in a school, and each one must gain it 

 for himself in his practice. 



But the greater his familiarity with scientific principles and the 

 experience of the past, the more able will he be to advance in 

 his profession, and to be trusted to assume responsibility ; in- 

 deed, if a man is ignorant of certain details and knows he is 

 ignorant, he can — and if he is the right kind of a man, he will — 

 take pains to learn them, if they bear on the work he has in 

 hand ; but if he is ignorant of scientific principles, it is very 

 likely that he does not know he is ignorant, or, if by good luck 

 he becomes aware of the fact, it is next to impossible for him to 

 devote the time and study necessary to correct his ignorance while 

 his mind is busy with his daily work. 



Moreover, a man who is not familiar with the scientific 

 principles which concern his work is not a safe man to trust 

 with responsibility ; for scientific principles are merely the 

 laws of nature, as far as known, as shown by the experience of 

 the past. 



Hence it is that the first and most important thing to be done 

 for the student is to give him a thorough drill in the scientific 

 principles which find their application in his profession. It is 

 in the school that this knowledge may best be acquired, since it 

 is only with great difficulty that principles can be mastered after 

 the student begins practice, and then as a rule but very im- 

 perfectly ; and this view is borne out by those engineers who 

 have been successful, and who have had to acquire their know- 

 ledge of scientific principles little by little, and as best they 

 could, during the practice of their profession. Too much cannot 

 be said by way of insisting that a thorough mastery of such 

 scientific principles far outweighs in importance anything else 

 that can be done for the student ; and this is so tnie, that it is 

 a decided mistake to neglect it in order to impart to him greater 

 skill in such processes as will probably engage his attention the 

 first year after he goes to work, as, for instance, to make him a 

 skilful surveyor, a finished machinist, or an elegant draughtsman. 

 Greater skill can far more easily be acquired after he goes to 

 work than can scientific principles, and if this mistake is made 

 the consequences w ill probably pursue him throughout his pro- 

 fessional life. 



The two fundamental sciences upon which the scientific 

 principles of engineering are especially dependent are mathe- 

 matics and physics, and no proper course in engineering can be 

 arranged without insisting upon these fundamentals. 



Let us begin with the subject of pure mathematics, and con- 

 sider what portions should be studied, how they shoulil be 

 studied, or rather how they should be known, and of what 

 service they are to the engineer after they have been mastered ; 

 bearing in mind that, in accordance with the opinions already 

 expressed, the course of study should be laid out with direct 

 reference to the needs of the engineer ; and that when it is so 

 laid out, it will, by the very fact that it leads to a definite end, 

 subserve best the purpose of true education, and hence of 

 developing the powers of the mind. Probably the best definition 

 of mathematics is that given by Prof. Benjamin Pierce, who 

 defined it as " the science of drawing necessary conclusions." 

 This definition, of course, includes formal logic, and hence em- 

 braces more than is ordinarily understood by mathematics. We 

 may assert, however, that the only fimction of mathematics is 

 to draw necessary conclusions from the assumed data. Mathe- 

 matics has nothing whatever to do with the correctness or in- 

 correctness of the data. If these are correct, the conclusions 

 deduced by mathematics w ill also be correct ; whereas, if the 

 data are false, the conclusions deduced by mathematics will be 

 false. 



Thus, if we require the sum o. a certain set of numbers, the 

 process of addition will give the correct result, provided the 

 lunnbers added are the right ones ; but if the numbers added are 

 not the right ones, the result of the addition will not be the one 

 desired, "indeed, we might comixue pure mathematics to a mill 

 —it will only produce gt)od meal when the corn furnished to it to 

 grintl is of good quality ; anil if the corn is poor, the meal pro- 



