NATURE 



[July iS, 1895 



approved himself sufficiently in the college examinations. 

 Scholars are practically required to become candidates 

 for honours in the natural sciences tripos, though the 

 new mechanical sciences tripos will no doubt attract 

 some. The new Salanion scholarships at Caius are, 

 indeed, specially intended for students of engineering. 

 It should be added that candidates for scholarships, who 

 are not yet members of the university, must be under 

 nineteen years of age ; there is no restriction of age in 

 respect of the science exhibitions. Though only nine 

 colleges specifically offer entrance scholarships in science, 

 an examination of the awards to the first, second, and 

 third year students shows that in many more good work 

 in science, as tested by university or inter-collegiate 

 examinations, does not go unrecognised. The large body 

 of medical students, now approaching five hundred in 

 number, is distributed over all the colleges, and their 

 presence has apparentK- brought home, even to the most 

 conser\ative, the fact that intellectual ability, high-minded 

 devotion to study, and social energy are not confined 

 to students of classics and mathematics alone. Thus, 

 though something remains to be done in certain quarters 

 .n the direction of placing science on an equal footing 

 with the older subjects as a fit object of college recogni- 

 tion and reward, it must be owned that a great advance 

 has been made within the last ten years. The natural 

 sciences tripos now attracts a larger number of candidates 

 than any other, and this notwithstanding that its standard 

 has steadily been raised. In the majority of the colleges, 

 distinguished eminence in this tripos has been admitted 

 as a qualification for a fellowship, and in not a few 

 instances governing bodies have felt the need of strengthen- 

 ing themselves on the side of science, and have departed 

 from Cambridge custom by selecting scientific members 

 of other colleges for this honour. 



The endowments for research, other than scholarships 

 and fellowships, have in late years been substantially 



ncreased. In addition to post-graduate studentships at 

 the larger colleges, such as the Hutchinson at St. John's 

 (physical and natural science), the Coutts-Trotter at 

 Trinity (physics and physiology), the Frank Smart at 

 Caius (botanyj, the university has of late received a 

 number of benefactions for the same purpose. The 

 Balfour studentship in animal morpholog^y, worth ^200 

 a year, the Harkness scholarship in geology about £.\<x>, 

 the Clerk Maxwell scholarship in physics about ^185, 

 the John Lucas Walker studentship in pathology £100 

 to l,yx>, the Isaac Newton studentships (three) in as- 

 tronomy ^200, and the Arnold Gerstenberg studentship, 

 for natural science students pursuing philosophical study, 

 about £S3i 3te among these recent foundations. They 

 are expressly intended to foster advanced study and re- 

 search, and they have alrc.idy produced excellent results. 

 The university still lacks the means of providing similar 

 encouragements for higher work in chemistr)', in anatomy 

 and anthropology, in botany, in mineralogj-, in physiology, 

 in pharmacology, and in scientific engineering. It is to 

 be hoped that the line of generous benefactors is not yet 

 extinct, and that some of these important subjects may 

 ere long receive the benefit of their munificence. The 

 new scheme for the promotion of post-graduate study 

 and research, which has received the approval of the 

 senate, and now only awaits the assembling of Parliament 

 for the sanction of the necessary statutes, will render 



such endowments opportune and fruitful. 



SCALE LIXES ON THE LOGARITHMIC CHART 

 'T'llK .kK.iiii.i IS iif logarithmic plotting for certain 

 ' i live for some time been recognised, 



and n'> to Mr. Human, logarithmically 



ruled paper < an i)f obtained ready made, the facility of 

 such plotting i^ greatly increased, so that there is all the 

 more reason on this account why it should become more 



NO. 1342, VOL. 52] 



common than it seems to be at present. It may perhaps 

 be well to point out shortly what the nature and effect of 

 logarithmic plotting is, and to contrast it with the more 

 common method on square-ruled paper. Instead of 

 paper ruled in equal squares, logarithmic paper is ruled 

 first in a scries of large equal unit squares representing 

 tenfold changes in the coordinates. Thus two units 

 represent 100, three units 1000, and so on. .Similarly the 

 squares are broken up fractionally and unequally into 

 a series of vertical and horizontal lines, whose distance 

 from the left or lower side of the square is equal to the 

 logarithms of the numbers 2, 3, 4, lifcc, and these are sub- 

 divided again logarithmically just in the same way that 

 a slide rule is subdivided. In fact, if logarithmic paper 

 is not available, logarithmic plotting can still be carried 

 out fairly expeditiously by pricking off distances direct 

 from a good slide-rule. The meaning of lines drawn 

 upon logarithmic paper is very ditierent from that upon 

 ordinary square ruled paper. For instance, an inclined 

 straight line ruled in the ordinaiy way represents the 

 equation V = <( -f- /u", whereas when logarithmic paper is 

 employed the corresponding line gixes )' = ax''. The 

 consequence is that whenever two quantities are related 

 so that one varies as any power, positive, negative, 

 integral, or fractional of another, a straight line drawn 

 in the proper positibn and inclination represents that 

 relation, the power being equal to the trigonometrical 

 tangent of the angle of slope of the straight line. If the 

 relation that is to be represented is less simple, if the 

 index changes gradually as either of the coordinates 

 changes, so that a curve has to be employed, then the 

 size and shape of the curve represents the law in the 

 abstract, and the position of the curve on the sheet the 

 actual numbers for the particular case and with the 

 I particular units ; a mere shift of the curve bodily upon 

 the chart, as pointed out by I'rof Osborne Reynolds long^ 

 ago, being all that is necessary to adopt the same law to 

 new circumstances or new units. 



One very important feature of logarithmic plotting is 

 I the fact that, not only is it practicable to include an 

 , enormous range (in .Mr. Human's sheets of four by five 

 squares of 10,000 and 100,000 in the two directions), but 

 [ the proportionate accuracy is identical in all parts, if it 

 is possible to draw or read to, say, I per cent, in one part 

 of a curve, the same figure is true everywhere. On the 

 other hand, in ordinary plotting the proportionate ac- 

 curacy of quantities near the origin is very small, while at 

 a great distance it becomes enormous. In order to assist 

 in the process of sliding any curve about on a logarithmic 

 chart so as to represent particular cases, special logarith- 

 mic scales may be ruled upon the sheet, having a suitable 

 magnitude depending on the index which connects the 

 result with the new variable, or what I have called scale 

 lines may be employed. In illustrating the laws which 

 connect the velocity and frequency of waves and ripples 

 at the Koyal .Society soiree, I exhibited these lines, and 

 showed how, in order to determine by inspection either the 

 velocity or the frequency of wa\ es and ripples of any wave- 

 length on the surface of any liquid under any acceleration 

 of gra\ ity, a single curve and two scale lines are all tliat 

 are needed. As by their use the logarithmic chart is made 

 I even more comprehensi\e than it is at present, I feel that 

 i no apology is needed for making use of the columns of 

 N ATl'KK to make them more widely known. 



As is well known, the velocity of surface waves on a 

 fluid depend both on gravity and on kinematic capillarity 

 or capillarity divided hv density. In the case of waves 

 of liirge size, capillarit) is of practically no account, and the 

 velocity dependsonly on the acceleration of gravity. Since 

 it depends on the square root of this acceleration, the line 

 on the logarithmic chart that represents the velocity of 

 waves of any size travelling under the influence of gravity 

 alone is straight, and slopes up so as to rise one square' 

 for every two that it moves to the right, its tangent is- 



