3o6 



NATURE 



\Aug. 20, 1874 



mits in itself no other mathematical comparison than that of 

 equality and inequality, and no other mathematical treatment 

 than simple increase or decrease, and in consequence it does not 

 admit directly of ordinary mathemntical investigation. Number 

 and extended magnitude, such as length, duration, iSrc, admits of 

 comparison by ratio, and of addition, subtraction, multiplication, 

 division, &c. Magnitudes of degree are only brought under 

 mathematical processes by means of conventional measurement. 

 That is to say, some number or extended magnitude, which is 

 found by experience to vary with the magnitude of degree, is 

 adopted eventually as the measure of that magnitude, and mathe- 

 matical processes are applied to the measure. It is incorrect, 

 however, to say that we take an extended magnitude which 

 varies in direct proportion with the magnitude of degree, as its 

 measure, because direct proportion of magnitudes which vary 

 together involves inequality of ratio of corresponding value, and, 

 as already stated, the proportion of ratio does not really subsist 

 between different values of a magnitude of degree, though from 

 the intimate mental connection between certain magnitudes of 

 degree and their measures, we often thinls it does. 



When, for instance, we say that the brightness of two equal 

 lights is double that of either, the statement is quite incapable of 

 proof by experiment, and is certainly not intuitional ; it is simply 

 conventional. If we agreed that the brightness of a number of 

 equal lights should be measured by the square root of the number, 

 we should have to consider that the brightness of light varies 

 inversely as its distance instead of as the square of its distance 

 from its origin, — a result against which nothing could be urged 

 but its practical inconvenience. Or, to take the example of a 

 magnitude of degree whose conventional movement is somewhat 

 less familiar to our minds : when we say that our expectation 

 of an event which happens on an average three out of four times 

 is double of our expectation of an event which happens once out 

 of four times, we are clearly using words in a conventional way. 

 The one belief is not really double of the other, but the average 

 by which we agree to measure it is double. 



Now with respect to force and mass, both magnitudes of de- 

 gree, it so happens that there are two almost equally natural 

 methods of measuring them consistent with, but nevertheless in- 

 dependent of, each other. Each of these may be conventionally 

 adopted, but in either case its consistence with the other can 

 only be demonstrated by experiment. 



If you agree to measure force as directly proportionate to the 

 acceleration it produces on a given mass, and mass as inversely 

 pioportionate to the acceleration produced by a given force, 

 then, to that extent, the second law of motion, and the law 

 which is sometimes adopted in place of Newton's third, are the 

 results neither of experience nor intuition, but simply of conven- 

 tion ; but then, on the other hand, it must be held that it is by 

 experience we come to the conclusion that the mass of two bodies, 

 as abcnc measured, is the sum of their two masses, and the weight 

 of two bodies the sum of their weights. If, on the other hand, 

 you conventionally measure forces by the number of equal weights 

 which will produce the same effect, and masses by the number of 

 bodies of equal mass which make them up, then clearly the truth 

 of the above portion of the laws of motion can only be proved 

 by experience. 



The mistake made by some mathematicians is that while 

 ostensibly assuming the one conventional measure of torce and 

 mass they tacitly assume the other, and then illogically profess 

 to demonstrate the necessary consequences of their own conven- 

 tions by reference to experience founded on the other. They 

 agree to measure force by the acceleration it produces in its own 

 direction on a given mass, and then profess to prove forces do 

 produce such proportionate acceleration by reference to experi- 

 ence, on the assumption that forces are to be measured by the 

 number of equal weights or other forcEs which will produce the 

 same effect. 



In the case of the first law of motion, mathematicians often 

 commit an error even more flagrant. To define force as that 

 which affects motion, and then to profess that it is proved by 

 experience that a body acted on by no force will remain at rest 

 or move uniform, is on the face of it absurd. As well might 

 Euclid, after defining a circle, have appealed to experience to 

 show that a figure, every point of whose circumference is not 

 equally distant from the centre, is not a circle. Or as well might 

 a doctor begin by defining intoxication to be a state produced by 

 taking alcohol, and then appeal to the experience of the Good 

 Templars to prove that in the absence of alcohol there is no 

 intoxication, 

 i^ . Herbert Spencer seems to me to be wrong, therefore, in con- 



cluding that our belief in the laws of motion is in the true sense 

 (if it has any true sense) intuitive ; but his error is the more ex- 

 cusable on account of the confusion of ideas involved in most 

 mathematical explanations of these laws. 



F. Guthrie 

 Graaff Reinet CoUege, Cape of Good Hope. June 21 



ORGANISATION OF THE FRENCH 

 METEOROLOGICAL SERVICE 



THE measures we alluded to in Nature, vol. x. 

 p. 294, with respect to the French Meteorological 

 Service, have been partially adopted, and will be shortly 

 followed by others. The Meteorological Service has been 

 divided between two astronomers — M. Rayet, who has 

 under his special care the magnetical map of France, the 

 official observations taken at the observatory, and the 

 several French stations ; and M. Froat, who has been ap- 

 pointed to investigate the great disturbances of the atmo- 

 sphere, to send warnings to the principal French seaports, to 

 publish the atlas, and correspond with the several depart- 

 mental commissions which have been already appointed. 

 These departmental commissions are appointed by the 

 prefect of each department, and funds are granted to them 

 out of the dtpartmental budget and voted by the Council- 

 General of each department. 



M. Leverrier issued, on August 5, a circular to these 

 general commissions, informing them that the printing of 

 the storm-maps, which had been stopped owing to the 

 country's calamities, was to be resumed. 



Special mention is made in this circular ot the hail- 

 storms which have been studied most carefully by MM. 

 Becquerel, father and son. Nothing has been done yet 

 to increase the efficiency of lightning conductors. 



The several departmental commissions, numbering 

 about ninety, including Algiers, have been grouped into 

 six natural regions. M. Ch. Sainte-Clair Deville has 

 been sent to Algiers to organise the meteorology of that 

 country, from the sea to the remotest parts of the French 

 possessions in the desert. He has not finished his tour 

 yet. He is General Inspector for Meteorology, and had 

 issued an order for altering the hours of observation, 

 which order was cancelled by the Ministry. 



Some arrangements have yet to be made with the navy 

 for the storm warnings. \'ery likely French seaports 

 will continue to receive warnings from England, which 

 are very popular, as well as warnings from their own 

 observatory. 



NOTES 



Mr. Bri.\n Hodgson, F.Z.S., has presented to the library 

 of the Zoological Society a large collection of original drawings 

 of Himalayan Mammals, made during his residence in Nepaul. 

 They are of much scientific value, as being in many cases taken 

 from the types on which his species are founded. 



M. M.'VREY has recently published the results of experiments 

 undertaken to determine by the graphic method what is the true 

 movement 'of the legs in walking. His results prove convincingly 

 that the brothers Weber were wrong in assuming that the 

 oscillation of the leg which is not in contact with the ground is 

 the same as that of a pendulum ; for when it is represented on a 

 uniformly moving plane, the line drawn is a straight and not a 

 curved one. The movement of the suspended foot is therefore 

 uniform, depending on muscular action, in combination with that 

 of gravity. 



Dr. Morrison Watson, Senior Demonstrator of Anatomy 

 in the University of Edinburgh, has been appointed Professor of 

 Anatomy in the Owens CoUege, Manchester. 



