813 



WEIGHT. 



WEIGHT OF OBSERVATIONS. 



8U 



a hook or ring attached to the upper end of the tube ; and the extent 

 of the motion of the spring, and consequently the weight of the body 

 suspended from it, are indicated by the degree to which the rod is 

 drawn out of the tube. For this purpose a graduated scale is engraved 

 upon the rod ; the divisions indicating the extent of compression pro- 

 duced in the spring by the application of known weights. Several 

 spring-balances on the same principle are made for various purposes. 

 That known as Salter's balance has a brass plate attached to the tube 

 or cylinder, within which the spring is enclosed, and a vertical slit 

 through the plate and tube. A scale is engraved on the face of the 

 brass plate, and the weight is indicated by a pointer which moves up 

 and down with the spring, with which it is connected through the 

 vertical slit in the tube. Martin's "index weighing-machine" acts 

 upon the same principle, but has a circular dial-plate and a revolving 

 pointer or index, resembling the hand of a clock. On the axis of the 

 index, but at the back of the dial-plate, is a toothed pinion, which is 

 turned by a straight rack attached to the vertical rod, which rises and 

 falls with the spring. The index remains in a vertical position when 

 the balance is unloaded, and deviates more or less from it when a 

 weight is attached to the hook. One advantage of thin construction 

 is that the point of the index traverses a much greater space than the 

 spring itself, so that a small movement of the spring becomes readily 

 discernible. 



Spring-balances with helical springs are applied to several useful 

 purposes besides that of ascertaining the weight of bodies. A spring 

 of this character is sometimes used to hold down the lever of the 

 safety-valve hi a steam-engine boiler, the movement of the index 

 also showing the pressure of the steam. Such an apparatus is 

 useful in a locomotive engine, the shaking motion of which might 

 derange a valve loaded with moveable weights. A helical spring- 

 balance forms also a good cable-stopper. When applied to the measure- 

 ment of muscular force, the tractive power of a locomotive carriage, 

 &c., one end of the cylinder in which the spring is enclosed is made 

 fast to an immoveable object, and the power to be measured in applied 

 to the sliding-rod. If used to ascertain the force necessary to draw a 

 carriage, the spring U placed between the carriage to be drawn and the 

 power employed to draw it. In using a spring-dynamometer for this 

 purpose, especially when the carriage is moved by animal power, some 

 inconvenience is occasioned by the vibration of the index with every 

 trifling variation in the force applied, to remedy which Mr. H. K. 

 Palmer contrived an apparatus in which the quick vibration of the 

 spring is checked by means of a piston moving in a cylinder filled with 

 oil. A very narrow space is allowed for the oil to pass between the 

 edge of the piston and the cylinder, so that a considerable resistance is 

 opposed to the motion of the piston and the springs, and the index 

 consequently represents the mean amount of force applied without 

 being affected by sudden variations. 



The ingenious method adopted by Mr. Martin for transmitting the 

 motion of a spring to an index moving upon a circular dial-plate, is 

 applicable to spring-balances of other than the helical construction. It 

 was used by M. Hanin, a French gentleman, who was rewarded by the 

 Society of Arts, in 1790, for an apparatus for showing at one view the 

 weight of an object according to several different scales or systems of 

 weights. His machine which ia described and figured in the ninth 

 volume of the Society's ' Transactions,' consists of a dial-plate, on 

 which are marked several concentric circles, divided according to the 

 systems of weights used in different countries, and an index moved by 

 a rack and pinion, as before described. The spring, instead of being 

 of a helical form, is semicircular ; its upper extremity being firmly 

 attached to the back of the dial-plate by means of screws, while its 

 lower end is attached to the hook which carries the weight, and the 

 sliding rack by which the index is moved. Marriott's patent weighing- 

 machine is similar to that of M. Hanin, but the spring is a perfect 

 ellipsis, with its longer axis laid horizontally. The stem to which the 

 ring for holding the apparatus is attached is fastened by a nut and 

 screw to the middle of the upper side of the spring ; and the rack, 

 with the hook which holds the article to be weighed, to the correspond- 

 ing point on the lower side of the spring. The spring, rack, and 

 pinion are enclosed in a circular box at the back of the dial-plate, the 

 periphery of which serves as a stop to prevent the spring from being 

 overstrained. A similar apparatus, contrived by M. Itegnier, has been 

 used as a dynamometer, as well as a weighing-machine. 



A scale plate or dish may be added when necessary to any of the 

 spring weighing-machines which have been described. On account of 

 the absence of weights, and the great simplicity of their application, 

 spring-balances are useful in cases where extreme accuracy is not 

 required, especially when a portable weighing-machine is desirable. 

 Machines for ascertaining the weight of the human body are often 

 made on this principle, a kind of chair being suspended from the 

 spring. 



\V KIOHT. There is nothing to say on the feeling of weight after 

 what has been said in PRESSURE ; nor is it possible to give any idea 

 which will be half so good as that which presents itself in raising a 

 heavy body from the ground. The measure of weight is weight itself 

 [BALANCE], and two weights are equal which counterpoise each other 

 when placed at the ends of equal arms of a self-poising lever. 



The weight of a body, that in, of a given bulk of known substance, 

 Is referred to that of water by what is called the SPECIFIC GRAVITY of 



the substance. It is said, for example, that the specific gravity of 

 ivory is 1826, when that of water is 1000. This means that any bulk 

 of ivory is more weighty than the same bulk of water in the proportion 

 of 1826 to 1000. When the specific gravity of water is called 1, that 

 of ivory is 1 '826. Since a, thousand ounces avoirdupois of water are 

 nearly a cubic foot, a more popular notion of the meaning, of specific 

 gravity may be given, in this way : To say that the specific gravity of a 

 substance is 1'826, that of water being 1, is to say that a cubic foot of 

 it weighs 1'826 x 1000, or 1826 ounces nearly. More correctly, from 

 1000 times the specific gravity (water being 1), subtract three times 

 that specific gravity, and add its 73rd part : the last step may be left 

 out for common purposes. Thus, the specific gravity being 4'817, 

 4-817 x 1000 4-817 x 3 ia 4802'549, the number of ounces in a 

 cubic foot. 



But it is to be remembered, when weight is to be very accurately 

 taken, that everybody is buoyed up to a certain extent by the air ; and 

 the weight of a body in air is less than it would be in a vacuum by 

 the weight of its own bulk of air. Now the air varies in weight [AIR"] 

 in a manner which may be ascertained nearly by the indications of the 

 barometer. Properly speaking, it varies in a manner depending upon 

 the superincumbent pressure, the temperature, and the quantity of 

 moisture contained in it. A hundred cubic inches of dry air, when the 

 barometer is at 30 inches and Fahrenheit's thermometer at 60, weigh 

 31"012 grains. In measuring standards of weight, therefore, close 

 attention must be paid to the state of the air at the time of weighing 

 and to the substance weighed. If an iron weight balance a wooden 

 one in a given state of the atmosphere, for that very reason there can- 

 not be strict equilibrium in any other state of the atmosphere ; wood 

 being at least seven times as bulky as iron, the effect produced on the 

 weight of the wood by the alteration of the state of the air is at least 

 seven times as much as that produced on the iron. 



WEIGHT OF THE AIR. [AiR.] 



WEIGHT OF THE EARTH. [EARTH, MEAN DENSITY OF THE ] 



WEIGHT OF OBSERVATIONS. This article is only for the 

 reference of the mathematical student; in MEAN will be found as 

 much of it as an arithmetician can use by rule. 



This term was first applied in the manner stated in the article MEAN, 

 An observer decided the relative merit of his observations by his 

 unassisted recollection of the impression made by them upon his mind 

 at the time, and affixed weights to them ; that is, supposing A,, A 2 , &c., 

 to be the n results of observation, he attached numbers c,, c a , &c., pro- 

 portional to their presumed goodness, and used 2eA-f-2c instead of 

 2 A-^, for the average. Instead of c,, c t , &o., any numbers propor- 

 tional to them may obviously be used : and in applying the higher 

 branches of the theory of probabilities, it was found that a certain 

 mode of obtaining c u c v &c., while it gave -the above mode of using 

 these numbers in the formation of an average, made them applicable 

 to other important uses. We here give a sketch of the results of this 

 method in its simplest parts. 



1. When a number of discordant observations, made under circum- 

 stances hi which positive and negative errors are equally likely, do not 

 differ much from each other, and when it ia exceedingly unlikely that 

 the truth con differ much from the observations, it may be presumed 

 that the chances of the error .of any one of those observations 

 lying between x and x + d x, and between a and 6, are severally of 

 the forms 



and 



where c ia a constant dependent on the goodness of the observations, 

 and TT = 3-14159..., e= 271 828. ..., as usual. Even if this law of error 

 do not exist, it is found that the treatment of a considerable number of 

 obgervatione, whatever * may be the law, is reducible to the same rule's 

 as those derived from this law, which is now universally assumed 

 by those observers who apply the theory of probabilities to then" 



2. The constant c is called the weight of the observations, and 

 depends upon the various circumstances which determine their good- 

 ness or badness. The greater it is the better the class of observa- 

 tions to which it applies. It is approximately found, for a given class 

 of observations, as follows : Subtract each of the observations from 

 their mean, and let e lt e.,, &c., be the results; then c=n-=-22e". The 

 sum of the squares of the departures from the average may be found 

 by diminishing the sum of the squares of the observati'sns by n times 

 the square of the mean ; and before doing this any convenient quantity 

 may be struck off from all the observations, provided it be also struck 

 off from the mean. 



8. The probable error is that within which, taken positively and 

 negatively, there is an even chance an observation shall lie. Thus if 

 there be an even chance (A being the true result) for the result of an 

 observation lying between A a and A + a, then a is the probable error 

 of an observation. To find the probable error, divide -476936 by the 

 square root of the weight. 



* That Is, provided the law be (rach aa common enso can admit, as repre- 

 senting what actually takes place in human observations. It would not apply, 

 for example, to a case in which the larger the error the more likely was it to 

 happen. 



