42 



NA TURE 



[May lo, 1.894 



cision of such values as these, the average delicacy of female 

 discrimioation li«tween the two points is to that of the male, in 

 a ratio that lies somewhere between 7 to 6 and S to 7, or 

 thereabouts. It will be recollected that the former ratio was 

 that between the median female and the median male. 



The variahilily of the discriminative power appears from the ' 

 observations to he distinctly higher amon^j females than among 

 males. Measuring it in the usual way, by the half difference 

 between the two quarliles, which is the same thing as the 

 prohal'U error o{ a single observation, or else by any multiple 

 of this, as by the mean error, we find that the variability among 

 females is to that among males as 370 to 325, say as 8 to 7. 

 It is in consequence of this that so large a difference is shown 

 between the relative sensitivity of the two sexes, at the right 

 and left extremes of their respective curves in Fig. 2. We find 

 from Table II. that the value of C— ^at the 1st decile is 23 milli- 

 metres, and at the 9th decile it is only 07, the differences 

 between ihe intermediate pairs decreasing regularly. The 

 regularity of the decrease is not apparent in the actual obser- 

 %'ations,as shown in Fig. I, nor in Table I., still there is nothing 

 in what we see there that is incompatible with Fig. 2, while 

 Ihe fact of the difference between the right ends of the traces 

 being much less than that between the left, is conspicuous. 



Is it. however, a physiological fact that women are more 

 variable than males in respect to discriminative touch, or are 

 the observations affected by any extraneous cause of variability ? 

 I think that the recorded variability may in a very small part 

 lie accounted for by the fact that women vary much more than 

 men in the exercise of sustained attention. Carelessness would 

 affect the results in the same direction as diminished sensitivity. 

 Thus suppose one part of a large number of persons who were 

 all really alike in sensitivity, to be very careless, and the re- 

 mainder to be scrupulously careful : the mind^ of the careless 

 would be apt to wander ; they would then fail lo notice the 

 first just-perceptible sense of doubleness, and would appear, in 

 consequence, to be more obtuse than the careful ones. Though 

 the range of variability was in reality ;/;'/, the existence of care- 

 lessness would introduce variability into the records. Some 

 women are religiously painstaking, as much so as any men ; but 

 the frivolity of numerous girls, and their incapacity of, or un- 

 willingness to give, serious attention, is certainly more marked 

 than among men of similar ages. Women may, however, be 

 really more variable than men in respect to sensiiivity, because 

 they seeui more vaiiable in a few other respects, such as in stature 

 and obe-ity. Many more very tall girls aie to be seen now a- 

 days among the upper classes than foimerly, but the run of the 

 statures among men has not altered <|uite so much. The 

 multitude of extraordinarily obese women who used to frequent 

 Vichy for the cure of fatness, were wonderful to behold ; but 

 they are no longer to be seen in their former abundance, as 

 the fashion of treatment has changed wiihin recent years. 

 Again, it appears that women vary much more widely than men 

 in respect of their morality ; to which assertion I would quote 

 Tcnny-nn as a corroborative witness, who writes as follows, in 

 Merlin's soliloquy on the character of \ivien : — 



" Formeo at most dilTer as heaven and cinh, 

 Itul women l>ett and wor»t as heaven and hell." 



Since Fig 2 is true lo scale, it is easy to utilise it 

 for ascertaining Ihe class-place of any man or woman in 

 respect to the form of sensitivity now in question. The whole 

 process would be as follows : — Take a pair of compasses, 

 and find with them by experiment the just-perceptible 

 interval across on the nape of the neck of the person tested ; 

 then apply the compavses, to Fig. 2, keeping one (the lower) of 

 its points always on the base line of the Fig., and holding the 

 compasses so that the line joining its points shall be perpendi- 

 cular to that base line. .Slide the lower point of the compasses 

 along the base line until the upper point touches the male or 

 female trace, as the cise may be ; then read off the grade at 

 which the lower point Htan'ls on the base line. .Suppose it to 

 be 35 ; wc thereby learn that 35 jicr cent, of Ihe same ses have 

 more wDsilivity than the pernon tested, and that 65 per cent, 

 have le»<. .Similarly for any other value. 



It would, I think, lie well worth the while of an inquirer to 

 repeal these tests, to revise my result*, and to pursue the subject 

 m ' ' " ' '■ rr- should feel ilisposed to do so, I would 



«i;. ikc his measurements with the cheap 



for - .. , - - , in common nse by carpenters. The 



legs arc connected not by a joint, but by a spring which tends 

 to separate them, and they arc brought together to any desired 



interval by turning a screw with the finger and thumb, whidi I 

 overcomes the spring. The interval between the points could < 

 ea-ily be measured on a separate scale ; all the more easily, if ] 

 there were a slight depression at the zero point of the scale, in - 

 which one leg luight be securely rested. 



Francis Gaiton. 



THE RELATION OF MATHEMATICS TO 

 EA'GfNEERfNG.^ 



A r ATIIEM.VTICS has been described in this room as a good 

 ■^ servant but a bad master. It will be mv duty this even- 



ing to prove by suilalde illustration the first half of the proposi- 

 tion, and to show the service mathematics has rendered and can 

 render to en'^ineers and engineering. 



In our charter the Institution of Civil lingineers is defined as 

 " A society for the general advancement of Mechanical Science, 

 and more particularly for promolin>; the acquisition of ili 

 species of knowledge which constitutes the profession of a Cn 

 Engineer, being the art of directing the great sources of power 

 in nature for the use and omvenience of man, .as the n.eans of 

 production and of traffic in stales boih for external and internal 

 trade, as applied in the construction of roads, bridges, aqueducts, 

 canals, river navigation and docks, for in:ernal intercourse and 

 exchange, and in the construction of ports, haibours, moles, 

 breakwaters and lighthouses, and in the art of navigation by 

 artificial power for the purposes of commerce, and in the con- 

 struction and adaptation of machinery, and in the drainage of 

 cities and towns." No better definition can, I think, be found 

 for our profession than that it is the art of directing the great 

 sources of power in nature for the use and convenience o( man. 

 It covers all that the widest view of our work can include, and 

 it excludes those applied sciences, such as medicine, which deal 

 with organised beings. Mathematics has to deal with all 

 questions into which measurement of relative magnitude enters, 

 with all questions of iiosition in space, and of accurate deler- 

 minalion of shape. Kngineering is a maihcniaiical science in a 

 ])eculiar sense. Medicine, the other great profession of applied 

 science, has but little lo do with questions of measurement of 

 magnitudes, or of geometry ; but the engineer finds them enter 

 into everything with which he has to deal, and enter in the most 

 diverse ways. The thing he has lo determine is that the means 

 he employs is enough and not unnecessarily more thar. enough 

 to attain the end in view. For this he must numeric.illy 

 measure the end and the means and see that they are justly pro- 

 portioned to each other. It is useless this evening to waste lii 

 proving, what all will admit, that no one can be even 11 

 humblest engineer wiihout a knowledge of arithmetic .uil 

 enough of geometry to enable him to read a drawing, that some 

 trigonometry, some rational mechanics and a knowledge of jmo 

 jections, is a very useful part of the menial equipment ni 1 

 draughtsman. It is hardly necessary to call attention ic. tlic 

 great economy in the labour of calculations effected by the u^l 

 ol logarithms, a mathematical instrument for which we arc 

 indebted to Napier. We may with more profit examine what 

 u>e the higher mathematics can be to the practical engineer, 

 and what has been done in the p.ist for engineering by its aid. 



Judging from etymology, mathematics must have been begun 

 by engineers ; for surely geometry is the work of the canh 

 measurer or land surveyor. Hut since the prehistoric limes 

 when geometry was initialed, engineers have not added much 

 that is new to mathematics. They have rather sought anwUx 

 the stores of the malhematician and seiecleil the hamliest iiialhc 

 uialical tool they could find for the particular purpose of the 

 moment, but have done litile or nothing in return in the way of 

 improving the tools which they borrow. In this respect the re- 

 l.ilion of engineering to mathematics (iiffcrs much from its 

 relation lo expcrimenlal physics. In electricity, magnetism and 

 heat, enginceis have from their pr.aclical experience repeatedly 

 cotreclcd the ideas ol the theorists, and have started the science 

 on more accurate lines. If our subject to night had been the use 

 of the practical applied science of engineering in promoling the 

 development of puie malheniatics, we shoulil speedily find iti-' 

 there w.as hardly any ni.iterial for discussi<m. The acc" 

 being all on one side, let us sec to what the debt of the engiri' 

 to the mathemaiician amounts. 



There is no depattmcnt of practical engineering in which the 



1 The " J.imes lorredt " Lecture, delivered at the Intliiution of Civil 

 Enginecrii, by I)r. Joiin l-lopkinsuti. F.R.S., on M.-iy 3. 



NO. I 2S0, VOL. 50J 



