v : OKKKSPONDENCK IX FRENf'If. 



measured by tho product of tho mass and the velocity, that ia 

 by tho momentum generated. 



momentum produced is therefore proportional to the pres 

 ire. Hence the law is frequently stated thus : When pros 

 sure produces motion in a body, tho momentum generated is 

 proportional to tho pressure. Momentum, then, is the measure 

 of moving force, as velocity is of accelerating force. From this 

 we find a way of comparing those two. Tho latter is measurec 

 I'.v ill.- velocity, irrespective of tho mass, and as the pressure 

 which is tho moving force, imparts the velocity to the body, ii 

 i- . 411:1! i i the mass multiplied by this velocity. That is 

 .-. = mass x accelerating force. Hence the moving 



i by the mass gives the accelerating force. 

 I'Y.iin this we can calculate the dynamical unit of force, thai 

 tint foivo iv. inirod to cause the unit of mass to move one fooi 

 ml, which force we stated in our second lesson to be 

 7'85 grains. 



'I'd. unit of mass is one cubic inch of distilled water, and this 

 nearly 253 grains. Now the accelerating force of gravity 

 produces this weight is 32*2, that being, as we shali 

 shortly see, the velocity a falling body acquirer in one second. 

 But the velocity we want is only 1 or ~, of this. Hence the 

 unit of moving force is 253 gr. x .- or 7'85 gr. 



The apparatus usually employed to prove the third law of 

 consists of what is known, after its inventor, as 

 Atwood's machine. It consists 

 essentially of a fine cord, which 

 passes over a wheel or pulley, and 

 to each end of which equal weights 

 are fastened. 



In Fig. 96, A represents the wheel 

 over which the cord passes, a small 

 groove being turned on the edge to 

 receiveit. Inorderto reduce friction, 

 which would materially interfere 

 with the accuracy of the results ob- 

 tained, this wheel does not turn in 

 bearings, but its axle rests upon the 

 rims of four others called friction 

 wheels. These turn with the axle, 

 and so far diminish friction that its 

 effect is scarcely noticed. One of 

 the pillars which support these 

 wheels is accurately graduated to 

 inches and fractions of an inch. 



A hollow ring, D, and a stage or 

 table, E, are also fixed to clamps 

 sliding on this pillar, so that by 

 means of small thumb-screws they 

 can be adjusted at any height and 

 distance from each other that may 

 be desired. 



A pendulum of such a length as 



to tick seconds, with a small dial to register the number, is 

 fixed on another support at H. A catch is also fixed above D, 

 to hold w till it is allowed to fall. There are several minor 

 details of construction which have to be attended to, but they 

 need not bo explained here. 



Since w and w' are equal they will balance each other, and 

 no motion will ensue ; but if we now take a small bar of metal, 

 F, and lay it across the top of w, it will cause it to overbalance 

 w', and to descend with an accelerating velocity until it reaches 

 the ring D, when, the bar being too long to pass through, will 

 rest upon it, and w will continue to travel onwards with the 

 momentum it has acquired. Now tho weight moved is clearly 

 the sum of the weights of w, w', and F, aud the moving force 

 is the weight of F ; and by a series of experiments it is found 

 that the velocity with which w descends is always in the propor- 

 tion of the weight of F, divided by the total weight moved. For 

 instance, make w and w' each to weigh 7$ oz., and F a quarter of 

 an ounce : tho velocity will be represented by fa, the mass moved 

 being 16 oz., or 64 times the moving force. Now diminish each 

 of the weights to 7J oz.. and make F half an ounce. The mass 

 moved will remain the same as before, but the moving force 

 will be as large again as it was, and we shall find the velocity 

 will he represented by fa, that is, it will be twice as great as it 

 was. In other words, if the mass remain the same, a double 



preMnro is required to produce a doable Telocity, a triple 

 pressure three times the velocity, and BO on. 



Now let the mass be doubled, the moving force remaining 

 the same. Make w and w' 15joz. each, and v half an ounce, the 

 velocity will now be /r, or the same as it was at first. 80 that, 

 if the mass be doubled, a doable pressure is required to produce 

 the same velocity. We see, then, that whether the mass or 

 the velocity be increased, the pressure most be increased in the 

 same proportion, and therefore that the pressure is proportional 

 to the mass multiplied by the velocity, i.e., to the momentum, 

 and this ia what the third law of motion assert*. 



CORRESPONDENCE IN FRENCH. II. 



6. REPLY TO LETTEE OF INQUIRY AS TO SOLVENCY OF A 



FIRM. 



Pan*, August 19, 1882. 

 Messrs. Merivale Brothers, Havre. 



Gentlemen, We beg to acknowledge the receipt of your 

 letters of tho 26th of July and 19th inst. 



Although we say that the firm H. Smith Bros, is sound, it is 

 but fair to tell you, in confidence, that their reputation is not 

 entirely above all suspicion ; that this suspicion attaches itself 

 chiefly to a want of delicacy and scruple in their business, of 

 which a number of people have from time to time raised com- 

 plaints, so as to diminish the credit which the firm used to enjoy. 



Wo cannot, however, limit the extent of credit you may be 

 disposed to give them, except in so far the foregoing may de- 

 termine you. 



Please to send us particulars as to what is being done in 

 quinine in your city, and whether, as with us, it seems to go 

 down. We are offered some of superior quality at 4 francs 50 

 cents. Be good enough to send us all the particulars yon can 

 obtain of this drug, partly as to the monopoly, as to the news 

 from Peru, especially about the war, and as to the most favour- 

 able time for purchase. 



We are, Gentlemen, your very obedient servants, 



HENBY LAFITTE A Co. 



Paris, It 19, AoM, 1882. 

 Messieurs Merivale Freres, an Havre. 



Messieurs, Nous accusons reception de vos lettres du 26 

 Juillet et du 19 courant. 



Tout en vous disant que la maison H. Smith freres est 

 solide, nous devons aussi vons informer confidentiellement qn'elle 

 ne jouit pas entierement d'une reputation libre de toute cen- 

 sure ; que cette censure porte sur un manque de delicatesse 

 et de scrupule dans leurs affaires, dont bon nombre d'individus 

 se plaignent, de maniere a diminuer le credit dont jouissait 

 autrefois cette maison. 



Nous ne pourrions done vous fixer sur 1'etendue du credit 

 a leur accorder sinon par ce que nous venons de dire. 



Veuillez bien nous informer comment va le commerce de 

 a quinine snr votre place et nous dire si, comme ici, cet article 

 semble devoir flechir. On nous en oflre, de belle et bonne 

 qualite, a 4fr. 50o. Ayez la bonte de recueillir sur cet article 

 ,ous les renseignements que vous serez a memo de vous procurer, 

 ant sur le monopole, que sur les nouvelles qui arrivent du Pcron, 

 an sujet de la guerre, et sur le moment lo plus favorable pour 

 'air" des achats. 



Agreez, Messieurs, 1'assuranco de notre parfaite consideration, 



HENRI LAFITTB & C. 



7. LETTER OF INQUIRY AS TO STATE OF MARKETS UNDER 

 ADVERSE CIRCUMSTANCES. 



Amsterdam, May 2nd, 1882 

 Messrs. J. T. Van Praat & Co., London. 



Gentlemen, The latest news from America has overcast the 

 commercial horizon and created a panic in our city. We tremble 

 or the consequences which such a state of things may produce. 

 ["he best houses are shaking, and we are momentarily expecting 

 a general suspension. We do not know how your markets are, 

 and in any case it -would not become as to give you any advice ; 

 we merely throw out a hint, that the consequences of these un- 

 oward circumstances must be felt, with yon, as in all the great 

 industrial centres. 



Be good enough to give us some information as to what yon 

 are doing, what you fear or hope, for we are somewhat uneasy 



