MECHANICS AND USEFUL ARTS. 21 



THE SIZE OF A DROP OF LIQUID. 



The size of a drop of liquid is often spoken of as a definite quantity. 

 In a paper on this subject by Mr. Tate, in the Philosophical Maga- 

 zine, it is shown that not only the size but the weight varies with the 

 diameter of the tube, and the density, temperature, and chemical 

 composition of the liquid itself. He gives the results of experiments 

 which show that, 1. Other things being the same, the weight of a 

 drop of liquid is proportional to the diameter of the tube in which it 

 is formed. 2. With regard to capillarity, the weight of the drop is 

 in proportion to the weight of water which would be raised in that 

 tube by capillary action. 3. The augmentations of weight are in 

 proportion to the diameter of the surfaces on which the drops are 

 formed. 4. The weight of a drop is diminished by an augmentation 

 of temperature. 5. Independent of density, the chemical composi- 

 tion of a liquid affects the weight of its drop in a remarkable man- 

 ner. 6. In different solutions of common salt and other natural 

 salts, the augmentation in the weight of the drop is in proportion to 

 the weight of dry salt in solution. The foregoing principles are 

 supported by tabulated statements. 



THE FRACTION 3,14159. 



The celebrated interminable fraction 3 '14159..., which the mathe- 

 matician calls TT, is the ratio of the circumference to the diameter. 

 But it is thousands of things besides. It is constantly turning up in 

 mathematics : and if arithmetic and algebra had been studied with- 

 out geometry, n must have come in somehow, though at what stage 

 or under what name must have depended upon the casualties of alge- 

 braical invention. As it is, our trigonometry being founded on the 

 circle, n first appears as the ratio stated. If. for instance, a deep 

 study of probable fluctuation from the average had preceded geome- 

 try, n might have emerged as a number perfectly indispensable in 

 such problems as - What is the chance of the number of aces lying 

 between a million -f- #, and a million x, when six million of throws 

 are made with a die ? I have not gone into any detail of all those 

 cases in which the paradoxer finds out, by his unassisted acumen, 

 that results of mathematical investigation cannot be : in fact, this dis- 

 covery is only an accompaniment, though a necessary one, of his par- 

 adoxical statement of that which must be. Logicians are beginning 

 to see that the notion of horse is inseparably connected with that of 

 non-horse : that the first without the second would be no notion at 

 all. And it is clear that the positive affirmation of that which contra- 

 dicts mathematical demonstration, cannot but be accompanied by a 

 declaration, mostly overtly made, that demonstration is false. If the 

 mathematician were interested in punishing this indiscretion, he 

 could make his denier ridiculous by inventing asserted results which 

 would completely take him in. 



More than thirty years ago I had a friend, now long gone, who 

 was a mathematician, but not of the higher branches: he was, inter 

 alia, thoroughly up in all that relates to mortality, life assurance, &c. 

 One day, explaining to him how it should be ascertained what the 

 chance is of the survivors of a large number of persons now alive dy- 



