40 



NATURE 



[Nov. 13, 1879 



14 lbs.) and by the nasal bone not diminishing so rapidly 

 in size. The mountain fox (Vuipes lagopus, L.) is very 

 common. The common fox {Vulpes vulgaris, Gray) 

 appears also to be common. A red fox, shot in L ctober, 

 differs considerably from the common, and approaches 

 the mountain fox in several particulars. The fox's food 

 during winter appears to consist of hares, ptarmigans, 

 and lemmings, t f lemmings three species were met 

 with, My odes obensis (the most numerous), M. tfrquatus, 

 and Arvicola obscurus. The Tchuktches state that a 

 little mouse also occurs, which Nordquist supposes to be 

 a Sorcx. The two lemmings often showed themselves 

 above the snow during winter, which was not the case 

 with Arvicola obscurus. The wolf was seen only twice. 

 The wild reindeer was also uncommon, traces of them 

 having been seen only once. Traces of the land-bear 

 were also seen, and the natives stated that they were not 

 uncommon in summer. The marmot (Arctomys) occurs 

 in abundance. An animal described by the natives as 

 living by the banks of streams is supposed to be the 

 common otter. Two weazel-skins were obtained from 

 the natives. It is not certain whether the ermine occurs 

 there. Only two marine mammals have been seen during 

 the winter, the Polar bear and the ringed seal (P/iocn 

 fiv/ida). The latter is caught in great numbers, and along 

 with fish and various vegetables torms the main food of the 

 natives. Of land birds there winter in the region only 

 three species, viz., Slrixnyclea, Corvus corax, and Lagopus 

 sttbalpina. The last-mentioned is the most common. On 

 December 14 two lar^e flocks of ptarmigan, one num- 

 bering about fifty, were seen about ten miles from the 

 coast. The raven is common at the Tchuktch villages. 

 Its first egg was obtained on May 31. The mountain 

 owl was seen for the first time on March 11, but according 

 to the natives, it is to be met with all winter. In open 

 places on the sea there occur during winter, according to 

 the natives, two swimmers, Uria Briinnichi and Uria 

 grylle. Besides these there possibly winter on the sea a 

 species of Mcrgulus and one of Fuligula, a specimen of 

 the former having been obtained on November 3, and of 

 the latter on March 9. 



{To be continued.) 



GALILEO AND THE APPLICATION OF 

 MATHEMATICS TO PHYSICS' 



TWO hundred and ninety-eight years ago to-day 

 ■*■ (November 5, 1581) Galileo Galilei, then a boy 

 between seventeen and eighteen, matriculated as a medical 

 student in the University of Pisa. At that time .Medicine 

 was perhaps the least satisfactory of scientific studies, and 

 though his family had influential professional connections, 

 the empirical maxims and the semi-metaphysical reasons 

 by which they were supported never caught the young 

 man's fancy or satisfied his intellect. We first hear of 

 him listening outside the door in which Ricci, the Court 

 mathematician of Florence, who happened to be spending 

 some time at Pisa with the Grand Duke, taught the pages 

 a little Euclid. For a couple of months Galileo neglected 

 his medicine, and greedily absorbed his Euclid through 

 the key-hole till he found some chance opportunity of 

 introducing himself to the Professor, who was delighted 

 with his new pupil. Ricci presented him with a volume 

 of Archimedes, and the great mathematician and physicist 

 of Syracuse became the spiritual father of the young 

 Italian student. In spite of the straitened circumstances 

 of his family, and the chances of fortune that awaited 

 him in a decorous prosecution of his regular medical 

 studies, he deserted them, and attached himself to Ricci. 

 Watching one day the long swing of a lamp hung from 

 the roof of a church, we are told that he noted the timts 



1 An Introductory Lecture, by William Jack. M.A., I.L.D., F.R.S E., 

 Professor of Mathematics in the University of Glasgow, formerly Fellow of 

 St. Peter's College, Cambridge. 



it took in oscillation after oscillation, and found that 

 though the arc through which it swept died down till it 

 was scarcely visible, the time it took from each farthest 

 right hand point to the succeeding farthest left hand point 

 of its sweep was always the same. He applied the know- 

 ledge I e had gained at once to the more accurate measure- 

 ment of the regularity of the pulse beats. The observation 

 of the student, and the immediate practical application of 

 it, was the sute forerunner of the greatness of the man. 

 He knew that Science is Measuremei t three centuries. 

 before Comtelaid it do mi as the definition of mathematics, 

 or Marks had been born to caricature the maxim in his 

 di] loma picture. 



At that time the Peripatetic philosophy was dominant 

 oxer Europe, and tyrann zed in Italy. The followers of 

 Aristotle naturally travestied the errors of their master. 

 In his own time Aristotle was a genuine observer of 

 nature, and, as Galileo afterwards said of him, he would 

 have been the last to dispute a fact because it contra- 

 dicted his preconceived opinions. His followers, who 

 were not observers, had constituted a universe on high 

 a priori principles. They taught that there were two 

 great classes of things perishable and terrestrial, one 

 heavy, tending by an irresistible law of their essential 

 nalure to the mathematical centre of the universe, the 

 other light, and tending irresistibly away from it. Things 

 imperishable and extra-terrestrial moved by a like neces- 

 sity in everlasting circles lound the centre of all things. 

 A body of 2 lbs. weight, having more tendency to the 

 centre than a body of 1 lb., must fall faster, and acquire 

 a greater velocity in an equal time. With a priori prin- 

 ciples like these observation was superfluous. Galileo 

 questioned them and put them to the examen rigorosum 

 of experiment. The explanation of the isochronism of 

 the larger or smaller swings of the pendulum lay in the 

 fact that though when the moving lamp started from a 

 higher point it had further to fall— it began to fall more 

 really perpendicularly and faster, and it swept through its 

 larger arc with a greater velocity at every point. When 

 he took two such pendulums of equal length, to the end 

 of one of which a lamp weighing 1 III. was fastened, and 

 to the end of the other a weight of 2 lbs., Galileo found 

 that their times of oscillation were the same. 



The Peripate ic dictum of the greater gravity of heavier 

 bodies was in contradiction with this simple fact. Galileo 

 took the two weights to the top of the hanging tower of 

 Pisa, and kt them fall. They fell at the same or practi- 

 cally the same instant. Though the simultaneous thud of 

 these t«o weights on the ground was the death-blow of 

 the Peripatetic assumption, it was not enough to convince 

 teachers who had grown grey in teaching it. But a 

 moment's thought now will serve to show us not merely 

 that it is so, but why it must be so. Instead of the mass 

 of 2 lbs., imagine for a moment that the 2 lbs are made 

 up of two single pound weights, each identical in shape 

 and material with the other mass of I lb., and that all 

 three drop together. All three will come to the ground 

 toge her. If the two pound weights are made to adhere 

 to each other by ever so thin a film of glycerine, there 

 will be no strain on the film, and they will not separate 

 If an imaginary section is cut through a single mass 

 of two pounds there will equally be no strain or shearing 

 force along that section. The tendency of the two single 

 lbs. downwards is twice as great as that of the 1 lb , but it 

 has to move two masses instead of one. Ten runners 

 who keep abreast of each other do ten times the work of 

 an eleventh runner on the other side of the course. Man 

 for man, each does the same work, and each man's work 

 has the same effect in producing the racing speed cf 

 each. An imaginary or real thread might tie the ten 

 together, but there would be no strain on the thread, 

 which would not snap, if their rates of running were the 

 same. 



Galileo often returned to the pendulum, and completely 



