312 



NATURE 



{August 1 6, 1877 



to discourse with full and equal knowledge of hyper-Jacobian 

 surfaces, the influence of temperature on the capillary constant 

 of dilute sulphuric acid, or the latest improvement in the con- 

 struction of aneroid barometers, some consideration would still 

 be due to their audience. And, long-suffering as British Associa- 

 tion audiences have often shown themselves to be, there is no doubt 

 that before a tenth part could be read of a report on the year's 

 work on the subjects included in this Section, the room would be 

 cleared and most of those who came to hear about mathematics 

 and physics would have gone to try whether they could not find 

 in Section E or F something appealing more directly to the 

 common sympathies of mankind. 



But although a serious report of progress would thus be both 

 impossible and unsuitable in the form of an Address to the 

 Section, it remains none the less true that such reports are in 

 themselves of the utmost scientific value, and, as has been 

 pointed out repeatedly, there are few ways in which the British 

 Association could more effectually fulfil its function of promoting 

 the advancement of science than by aiding in their preparation 

 and publication. But when one tries to think out in detail the 

 way in which the Association could do this, the practical diffi- 

 culties of the scheme are seen to be neither few nor trifling. It 

 may be sufficient to point out that there is no evident reason 

 why help of this kind should be afforded to one branch of 

 science rather than to another, and that the publication of reports 

 upon all branches would completely overtax the resources of the 

 Association. 



In the case of some important sciences, however, the work of 

 reporting recent advances is alieady undertaken by other bodies, 

 ^thus there are the "Abstracts" published monthly in the 

 Jourual of the Chemical Society, and there are the Zoological 

 KtYord, the Geological Record, and other publications of a like 

 nature,— but hitherto nothing of the kind has been done in this 

 country for those departments of science with which this Section 

 is specially concerned. But without attempting to commit the 

 Association to any burdensome outlay, or to any larger scheme 

 than it would be piacticable to carry out, it seems to me possible 

 that a systematic series of reports might be established in con- 

 nection with this Section which would have a very high value. 

 In the early volumes of the British Association's Transactions^^ 

 find more frequently than in recent ones, reports, not merely on 

 some special investigation, but on the recent progress and present 

 state of some more or less comprehensive branch of science. 

 Thus in the first four volumes we find the following, among 

 other reports, presented to this Section :— On the Progress of 

 Astronomy, On the Present State of Meteorology, On the Present 

 State of the Science of Radiant Heat, On the Progress of Optics, 

 On the Magnetism of the Earth, On Capillary Attraction, On 

 Physical Optics, On the Recent Progress and Present Condition 

 of the Mathematical Theories of Electricity, Magnetism, and 

 Heat. Now I venture to think that this form of the activity of 

 the Association might with great advantage be revived and 

 systematised. I would suggest, as a plan that seems to me 

 worth consideration by the Committee of this Section, the ap- 

 pointment of committees charged to report to the Section 

 periodically on the advances made in each of the chief depart- 

 ments of science of which we here take cognizance. For 

 example, to confine myself specially to physics, we might have a 

 committee on Optics, a committee on Acoustics, one on Heat, 

 one en Electricity, and so on. It would not be in accordance 

 with the usages of the Association to nominate these as standing 

 committees, but they might be made virtually such by annual re- 

 appointment. I would suggest that they should not report 

 annually, but at intervals of perhaps five or six years, the times 

 being so arranged that different committees should report in 

 different years, the report in each case being a systematic account 

 of all the work of any importance done on the subject and with- 

 in the period to which it related. In order not to make the 

 work too heavy, it would probably be needful to make each 

 committee comparatively numerous, so that individual members 

 might each undertake to report upon some limited part of the 

 general subject. Some one member of each committee would also 

 require to act as editor ; his function would be not merely to put 

 together the detached fragments sent in by his colleagues, but to 

 distribute to them the materials on which they would have to 

 report. For this purpose it would be needful that copies of all 

 the important scientific periodicals relating to Physics should be 

 supplied to the committee ; but besides providing these and 

 printing the reports, I do not see that the Association need be 

 put to any expense ; and if it were thought well to sell the 

 reports independently of the yearly volumes of the Associa- 



tion, probably a good part even of this expense might be 

 recovered. 



The mutual relations subsisting between the two great groups 

 of sciences, which we discuss in this .Section under the names 

 Mathematics and Physics, offer so many deeply interesting points 

 for consideration that, at the risk of reminding you how 

 admirably and with what fulness of knowledge the same subject 

 has been treated by more than one of my predecessors in this 

 Chair, I venture to ask your attention once more to a few remarks 

 on this topic. 



The intimate connection between Mathematics and Physics 

 arises out of the fact that all scientific knowledge of physical 

 phenomena is based upon measurements, — that is to say, upon 

 the discovery of relations of number, quantity and position, 

 of the same kind as those which form the subject matter of 

 mathematics. It is true that in studying physics we have to learn 

 much about the quality of phenomena and of the conditions 

 under which they occur, as well as about their purely quantitative 

 relations ; but even in the qualitative study of physical pheno- 

 mena we find it impossible to determine what is really charac- 

 teristic and to distinguish the essential from the accidental, 

 except by the aid of measurements. In fact if we take the most 

 elementary treatise upon any branch of physics that we can 

 meet with, a book it may be which aims at giving a purely 

 descriptive account of phenomena, we find, when we examine it, 

 that numberless careful measurements have been required to 

 establish the truth of the merely qualitative statements which it 

 contains- To take a simple and well-known example, the old 

 question whether the ascent of water in a pump was due to the 

 pressure of the atmosphere, or to Nature's horror of a vacuum, 

 was not conclusively settled by Torricelli's discovery that mercury 

 would not rise beyond a certain height in a glass lube, even to 

 prevent a vacuum being formed at the top of it, for the same 

 thing was already known about the water in a pump. But, when 

 he measured the height of the mercury-column in his tube and 

 found that if he multiplied it by the specific gravity of mercury, 

 the product was equal to thirty-two feet, the height to which, 

 as Galileo said (probaby between jest and earnest) nature's 

 abhorrence of a vacuum in a pump extended, it was clear that 

 the ascent both of water and of mercury depended upon the 

 particular depth of each liquid that was needed to produce 

 some definite pressure ; and when Pascal had persuaded his 

 brother-in-law to carry a Torricelli's tube to the top of the Puy de 

 Dome, and he had measured the height of the mercury-column 

 at the top of the mountain as well as at the foot, the proof was 

 completed that the pressure which determined the height of 

 both the water and the mercury was the pressure of the 

 atmosphere. 



Again, let us examine a still more familiar phenomenon, the 

 falUng of heavy bodies to the ground. So long as we 

 consider this merely under its general, or, as we may call them, 

 its qualitative aspects, we might reasonably infer that it is the 

 result of some inherent tendency of bodies ; and, so far from 

 its seeming to be true, as stated in Newton's " First Law of 

 Motion," that bodies have no power to alter their condition of 

 rest or of motion, we might infer that however indifferent they 

 may be as to horizontal motion, they have a distinct tendency 

 to move downwards whenever they can, and a distinct disincli- 

 tion to move upwards. But when we measure the direction in 

 which bodies tend to fall and the amount of the tendency in 

 different places, and find that these vary in the way that they 

 are known to do with geographical position and distance from 

 the sea level, we are obliged to conclude that there is no inherent 

 tendency to motion at all, but that falling is the result of some 

 mutual action exerted between the earth and the falling body. 

 For if we suppose falling to be due to any internal cause, we 

 must imagine something much more complicated than a mere 

 tendency to motion in one direction, else, how could a stone that 

 has alwaysfallen in one direction in England, fall in almost exactly 

 the opposite direction as soon as it is taken to New Zealand ? 



These two simple examples illustrate a principle that we meet 

 with throughout Physics: namely that, in the investigation of the 

 causes of physical phenomena, or in other words, of the connec- 

 tion between these phenomena and the conditions under which 

 they occur, the really decisive guidance is afforded by the study 

 of their measurable aspects. 



The consequence is that from the very outset of his investi- 

 gations the physicist has to rely constantly on the aid of the 

 mathematician, for even in the simplest cases, the direct results 

 of his measuring operations are entirely without meaning until 

 they have been submitted to more or less of mathematical 



