85 



ADHESION. 



ADHESION. 



86 



remainder only under m. Carry the hundreds, &c., to the next line on 

 the left, and so on. 



The addition of fractions is, in principle, as follows : We cannot 

 immediately express the sum of one-half of a foot and one-third of a 

 foot otherwise than by writing J 4- J of a foot. But if we recollect 

 that niie-half is three-sixth*, and one-third is tim-iietJa, it is evident that 

 the sum of one-half and one-third is fre-sixtkt. The rule, therefore, is ; 

 Reduce the various fractions to others of equal value, and having 

 the same denominator, add the numerators retaining the denominator : 

 or, multiply every numerator by every denominator, except its own ; 

 add the results, which gives the numerator of the sum : multiply all the 

 denominators together for the denominator of the sum. Thus, for 



+ ? + i which is $| 

 2x7x5= 70 1 

 3X3X5= 45 l.A\ld 

 4x3x7= 84 J 



199 numerator 

 3 X 7 X 5 = 1 05 denominator. 



To add decimal fractions, arrange them so that the decimal points 

 shall fall under one another, proceed as in common addition, and let 

 the decimal point in the sum total be placed under the other decimal 

 points : 



2-61 14-103 



04 1-04 



118 118 



2W 138-143 



To add algebraical quantities, write them all one after another, 

 without changing any sign, and connect the terms, which before had 

 no sign, with the rest, by the sign + . Thus a + 4 and a 2i added, 

 give a + b + a 26. This is the sum, which may be reduced to a 

 simpler form, by observing that 6 subtracted twice and added once, 

 is equivalent to 6 subtracted once, and that a is added to a. 

 The expression then becomes 2a 6. 



When the quantities are fractional, the preceding rule follows the 

 application of another similar to the rule in fractional arithmetic. 

 Thus, for 



7 + r the sum uf which in 



b a b n i _ (f 



a + 

 n X 

 b X 



(a 6) = a 1 at \ 

 (a + b) = nb + b' \ 



a* aft + ab + A 2 



Add 



a? + I 3 numerator 





(a + b) X (a 6) = a* 6* denominator. 



ADDITION OF RATIOS. A phrase which may, perhaps, at first, 

 puzzle the mathematical student who reads old books, and which we 

 therefore explain here. Take two ratios or proportions, say 3 to 7 and 

 5 to 9 ; the ratio of 3 x 5 to 7 x 9, or of 15 to 63 was formerly said 

 to be the mm of the ratios of 3 to 7 and 5 to 9. Similarly the ratio of 

 25 to 4 was said to be double of the ratio, or the duplicate ratio, of 5 to 

 2 ; that of 125 to 8, triple or the triplicate ratio, and so on. [RATIO ; 

 LOGARITHM.] The sum of the first ratios in any modern work would 

 probably mean } + J ; but the term ' sum of the fractions,' would most 

 likely be used in preference. 



ADHESION. This term has generally been employed to denote the 

 property by which two solids, a solid and a fluid, two solids and an 

 interposed fluid, or two fluids, remain attached to each other when 

 their surfaces are brought into contact. Adhesion may, in some in 

 stances, be considered as being but little if at all different from cohesion, 

 and dependent upon the same cause, while, in other cases, it appears to 

 be connected with, and probably to a considerable extent derived from 

 chemical affinity. When, for example, two surfaces of lead are pressec 

 together, the adhesion resembles mere cohesion, it acts at insensible 

 distances like that power, and no change of properties ensues in the 

 metal. If, however, the surface of a piece of lead is put into contact 

 with mercury, the two metals act upon and combine with each other 

 anil an amalgam is produced by virtue of the chemical affinity existing 

 between these two metals. There are other instances in which thi 

 adhesion is not distinctly to be referred to cohesion, and in which r 

 certainly does not depend upon chemical affinity, as when a plate o 

 glass adheres to the surface of mercury, or when liquids rise in smal 

 tubes by capillary attraction. 



Among the earlier attempts to determine the force of cohesion ar 

 those of Dr. B. Taylor, in a paper on Magnetism (' Phil. Trans.' 1721) 

 He performed various experiments to ascertain the force of adhesion 

 between wood and water, by determining the force in weight requirec 

 to separate them. He found it to be directly as the surface, and tha 

 a square inch of wood required fifty grains to raise it from the surfac 

 of the water. 



M. Achard (' Berlin Memoirs," 1776) made a vast number of exper 

 menU on the force of adhesion between plates of glass of differen 

 diameters, and many liquids, and upon the adhesion of twenty differen 

 substances with as many liquids. It had been supposed that adhesioi 

 was derived from atmospheric pressure, but M. Achard found that h 



arying the pressure no change occurred in the adhesive force of glass 

 ad water ; and that the adhesion of fluids to solids was uniformly in 

 le inverse ratio of the temperature. The diminution in the force of 

 dhesion by increase of temperatures was attributed by Guyton do 

 tforveau to the rarefaction of the fluid by heat, and the consequent 

 eduction of the points of contact in the same space. 



As the surfaces of the solids employed by Dr. Taylor and by M. 

 Lchard must have been wetted by the liquids, it has been objected to 

 heir experiments, and especially by M. Dutour in the ' Journal de 

 "hysique,' that they do not prove any adhesion between the solid 

 nd the liquid, but cohesion between the two portions of the liquid 

 vhich have been separated. If this objection be valid, then those only 

 an be considered as proper cases of adhesion, in which no particle of 

 ne substance remains with the other after the separation of their 

 urfaces, as when glass is separated from mercury ; M. Dutour found 

 hat a disc of glass 11 lines (French) in diameter adhered to mercury 

 with a force of 194 grams. 



M. Guyton published in 1777, in his ' Elemens de Chimie,' a series 

 f experiments on the force of adhesion between eleven metals and 

 mercury ; his method was as follows : The metals were made chemi- 

 cally pure, circular, and one inch in diameter ; they were all of the 

 same thickness, and were suspended from a ring in the centre at the 

 arm of an assay-balance and counterpoised ; the surface of the mercury 

 was then brought up to the plates, and the mercury was changed 

 ifter each experiment : the weights required to detach them were as 

 ollow : 



Gold 

 Silver . 

 Tin 



Lead . 

 Bismuth . 

 Platinum 



Grains. 



429 

 418 

 897 

 372 



282 



Zinc 

 Copper 

 Antimony 

 Iron . 



Cobalt . 



Grains. 

 204 

 142 

 120 

 115 



In these experiments the phenomena of adhesion appear to depend 

 ipon the degree of chemical affinity existing between the mercury and 

 -he metals applied to its surface. If the affinity were weak, the two 

 surfaces would separate by the application of a slight force. Indeed, 

 rf. Guyton himself considers that the weight required to separate the 

 different metals from mercury may directly express their affinity for 

 t. It will be evident on a moment's consideration that the degree of 

 adhesion is perfectly independent of the .densities of the different 

 metals. 



The sixty-third volume of the ' Philosophical Magazine ' contains a 

 paper by Mr. Bevan, in which the subject of adhesion appears to be 

 ionsidered in a point of view which had previously excited but little 

 attention, viz., the real force of adhesion of different nails when driven 

 nto wood of different species ; the weight, without impulse, necessary 

 to force a nail a given depth into wood, and the force required to 

 extract the same when so driven. The term adhesion in this case is 

 applied to the force, whether arising from friction, or cohesion, or 

 tartly from both, with which wood resists the drawing out of a nail. 

 rtr. Bevan has given a table of the adhesion, &c. of different kinds of 

 nails when driven into dry Christiania deal; in this table it appears 

 that a sixpenny nail, 73 to the lb., 24 inches long, forced 1J inch into 

 the wood, required 327 Ibs. weight to extract it ; the percussive force 

 required to drive the sixpenny nail to the depth of one inch and a half 

 into the dry deal, with a cast-iron weight of 6'275 lb., was four blows 

 or strokes falling freely through the space of twelve inches, while the 

 steady pressure required to produce the same effect was 400 Ibs. With 

 different kinds of timber the results varied greatly, and Mr. Bevan 

 concludes that a sixpenny nail driven two inches into dry oak, would 

 require a force of more than half a ton to extract it by steady pressure. 

 Mr. Bevan (' Phil. Mag,' and 'Annals of Philosophy,' vol. ii. p. 291) has 

 also determined the force required to draw screws out of different kinds 

 of wood ; the screws used were about two inches in length, '22 diameter 

 at the exterior of the threads, '15 diameter at the bottom, the depth of 

 the worm or thread, being '35, and the number of threads in one inch 

 = 12. These screws were passed through pieces of wood, exactly half 

 an inch in thickness, and drawn out from the following dry woods by 

 the annexed weights, beech 460 Ibs., ditto, 790 Ibs., ash 790 Ibs., oak 

 760 Ibs., mahogany 770 Ibs., elm C55 Ibs., sycamore 830 Ibs. The force 

 required to draw similar screws out of deal and the softer woods, was 

 about half the above. 



About twenty years ago, Professor W. R. Johnson undertook a series 

 of experiments on the adhesion of iron spikes of various forms, when 

 driven into different species of timber. The results of his experiments 

 were published in the ' Franklin Journal.' This inquiry was important 

 from the great use of spikes in the construction of railroads in America, 

 where the cheaper flat rail was preferred to the edge rail, and was 

 fastened to wooden sleepers by means of spikes. Whenever the speed 

 of a train was suddenly checked by the break, the friction of the wheel 

 tended to drive the rail lengthwise, and thus to force all the spikes 

 with which it was fastened into closer contact with the ends of the 

 fibres which had been cut through in driving them ; and, as this partial 

 or total dragging of the wheels may take place sometimes in one 

 direction and sometimes in the other, the spikes must be subjected to 

 alternate impulses on opposite sides. Indeed, the ordinary action of 

 the common locomotive produces a constant succession of these 



