Figs. 570 and 571.--Diagrams illustrating the decade plan of combining resistance coils. In this method the coils are connected in series and the arrangement avoids the disadvantage of the ordinary Wheatstone bridge in that the latter requires a large number of plugs to short circuit the resistances not in use, which introduces an element of uncertainty as to resistance of the plug contacts and the necessity of adding up the values of all the unplugged resistances in order to determine the total resistance in circuit. The necessary regular succession of values in a rheostat built on the decade plan can be obtained with either nine or ten coils per decade. The chief reason for using the latter number is found in the facility with which all the coils of one decade can be compared with one coil of the next higher decade, thus permitting the coils of a rheostat to be checked among themselves. Thus, the ten 1 ohm coils can be checked with a 10 ohm, the ten 10's with a 100, etc. In some sets the ten coils of a decade can be connected in series or in parallel, and it then becomes an advantage to have ten coils to a decade, since the coils in one decade in parallel equal one of the coils of the next lower decade. When these latter advantages are not required, and especially when dials or sliding switches are used, there is little or no advantage in using more than nine coils per decade, as shown in [fig. 570]. Here all the coils of the set are connected in series so that the circuit is never open. Thus it is a slight advantage to have permanent connections a, b, and c, because all the coils of a decade can be thrown in circuit by simply pulling out a plug, it not being necessary to insert it again, as would be the case if the a, b, and c connections were not used. Moreover, if any plug make bad contact, its effect is somewhat lessened by having this bad contact shunted by the remaining coils of the decade. Again, there are occasions where violent deflections of a galvanometer are prevented by not having the circuit entirely open when a plug is taken out.
The Decade Plan.--In this method of combining resistance coils, there are 9 or 10 one ohm coils for the units place, 9 or 10 ten ohm coils for the tens place, 9 or 10 one hundred ohm coils for the hundreds place and so on. Each series of coils of the same value is designated a decade. The connections are usually made as shown in figs. [570] and [571].
It is apparent from the figure that any value in any one decade can be obtained by inserting between a bar and a block, only one plug; moreover if several decades be in series, any value up to the limit of the set can be read off directly from the position of the plugs without having to add up the unplugged resistance as in the ordinary arrangement.
Fig. 572.--Two plug arrangement of ratio coils. Each of the ratio coils has one of its terminals connected to a common center which corresponds to the block marked C in the figure. The other terminal of each coil is connected to an individual block, there being one block for each coil. The bar B on one side of these blocks is joined to the rheostat and the bar A on the other side to an X post. In the ordinary use of this set of ratio coils two plugs only are used. One plug is inserted between the bar A and one of the blocks, 1, 1', 10, 10', etc., of the central row of blocks. The other plug is inserted between the bar B and any one of the other blocks of the central row. There are two ratio coils of each value. To obtain an even ratio as 1,000 to 1,000', one plug is inserted between the block 1,000 and the bar A, and the other plug between the 1,000 block and bar B, the ratio arms are reversed; that is, the 1,000 ohm coil is connected to the X post and the 1,000 ohm coil to the end of the rheostat. When uneven ratios are used, the same ratio can be obtained by four different combinations. To obtain the ratio one to ten, insert a plug between A and 1, and another between B and 10, or between A and 1', and B and 10, and get 1:10, or between A and 1, and B and 10', and get 1:10', or again, between A and 1' and B and 10', and get 1' to 10'. Other ratios are obtained in a similar manner. By using more than two plugs and connecting certain of the coils in parallel combinations, a large number of other ratios may be obtained. This arrangement offers a convenient method of measuring the sensibility of a bridge and galvanometer combination that is frequently applicable. If for instance the one ohm coil is used on either side after a balance has been obtained the one ohm may be shunted with the 1,000 ohm on the same side. This will make a variation of 1/10 of 1% and the galvanometer deflection may be noted for this variation. Similarly, the 1 ohm may be shunted with the 100 for a variation of 1%, or with the 10,000 for a variation of 1/100 of 1%. The ten ohm coil may be shunted with the 1,000 for a variation of 1% and with the 10,000 for a variation of 1/10 of 1%. In the arrangement of ratio coils, errors due to plug contacts are negligible because only two plug contacts enter the circuit, and with an even ratio, it is only the difference in the resistances of the two plug contacts that can affect the result. In measuring any of the ratio coils while in the box it is only necessary to connect to the bar C and to either the bar A or B and plug in the coils to be measured.
