﻿446 



Prof. K. W. Zenger on the Tangent -balance. 



The adjoined Table facilitates the operation for liquids ; for it 

 gives the natural tangent for the angle and also the density 

 when the normal liquid is sulphuric ether of specific gravity 

 0736 at 0°; a difference-table for ^° or 3' facilitates interpo- 

 lation. 



Table of the Density of Liquids for d Q = 0*736. 



u. tanw. A3'. Density. 



30 



1 



1 30 



2 



2 30 



3 



3 30 



4 



4 30 



5 



5 30 



6 



6 30 



7 



7 30 



8 



8 30 



9 

 9 30 



10 



10 30 



11 



11 30 



12 



12 30 



13 



13 30 



14 



14 30 



15 



15 30 



16 



16 30 



17 



0-0087, 



0-0175, 



00262 



00349 



00437 



00525 



00612 



0-0699 



0-0787^ 



0-0875 8 . 8 



0-0963 8 . 8 



01051 8 . 8 



01139 8 . 9 



0-1228 8 . Q 



01317 8 . 8 



01405 9 . 



0-1495L 



0-1584 s . o 



0-1673^ 



0-1764^ 



0-1853Q., 



0-1944g.j 



0-2035* 



0-2126L 



0-221 7 9 . 2 



0-2309 9 . 2 



0-2401 9 . 2 



0-2493 9 . 3 



0-2586 9 . 3 



0-2679 9<4 



0-2773 9 . 4 



0-2867L 



0-2962 9 . 5 



0-3057 9 . 6 



8-7 



8-7 



0745 

 0-753 

 0-762 

 0-771 



0-780 

 0-789 

 0-797 

 0-806 

 0-815 

 0-823 

 0-832 

 0-841 

 0-850 

 0-859 

 0-868 

 0876 

 0-886 

 0-894 

 0903 

 0-912 

 0-921 

 0-930 

 0-939 

 0-949 

 0-958 

 0-967 

 0-976 

 0-985 

 0-995 

 1004 

 1-013 

 1023 

 1-032 

 1042 



17 30 



18 



18 30 



19 



19 30 



20 



20 30 



21 



21 30 



22 



22 30 



23 



23 30 



24 



24 30 



25 



25 30 



26 



26 30 



27 



27 30 



28 



28 30 



29 



29 30 



30 



30 30 



31 



31 30 



32 



32 30 



33 



33 30 



34 



tan u. A3'. Density 



0-3153 9 . 6 



0-3249 q7 



0-3340 q7 



0-3443 q . 8 



0-3451 9 . 9 



0-3640 q . 



0-3739 10 . 



0-3839 10 - 



0-3939 ]0 -i 



0-4040] o-2 



0-4142 10 - 3 



0-4245 i0 -3 



0-4348 10 - 4 



0-4452 10 . 5 



0-4557,o-6 

 0-4663io-7 

 0-4770io-7 

 0-4877io-8 

 0-4986 10 - 9 

 0-5095 1V1 

 0-5206H-! 



0-5317 113 

 0-5430 n . 3 

 0-5543 lr5 

 0-5658 n . 6 

 0-5774 n . 6 

 0-5890 n . 6 

 0-6009 ! vg 

 0-6128^-! 

 0-6249!o. 2 

 0-6371 ^ 

 0-6494 12 . 5 

 0-6619 ]2 . 6 

 0-6715 lo . o 



1051 

 1061 

 1071 

 1-080 

 1-090 

 1100 

 1110 

 1120 

 1130 

 1-140 

 1-150 

 1-160 

 1-171 

 1-181 

 1192 

 1-202 

 1-213 

 1-224 

 1-234 

 1-245 

 1-257 

 1-268 

 1-279 

 1-290 

 1-302 

 1-313 

 1-325 

 1-337 

 1-349 

 1-360 

 1-373 

 1-385 

 1-398 

 1-410 



34 30 



35 



35 30 



36 



36 30 



37 



37 30 



38 



38 30 



39 



39 30 



40 



40 30 



41 



41 30 



42 



42 30 



43 



43 30 



44 



44 30 



45 



45 30 



46 



46 30 



47 



47 30 



48 



48 30 



49 



49 30 



50 



tanw. A3'. Density, 



0-6873 12 . 9 



0-7002 13 . 



0-7131 13 . 2 



0-7265 13 . 5 



0-7400 13 . 6 



0-7536 137 



0-7673 14 .; 



0-7813*; 



0-7954 4 4 . 



0-8098; 4 .g 



0-8243 14 . 8 



0-8391 



0-854 



0-86S 



0-8847 



0-9163 J.J 



0-9325 ^ 



0-9490 It 



0-9652 l b7 Q 



0-9827^" 



l-OOOO,^ 



1-0176 1; 



1-° 3 55 18 . 2 



1-0538 8 - 



10724 



15-0 

 15-2 

 15-4 

 157 



10913 

 1-1106 

 1-1303 

 11504 

 1-1708 

 1-1918 



18-5 

 18-9 

 19'3 

 197 

 '20 1 



,21-6 



1-423 

 1-436 

 1-449 

 1-462 

 1-476 

 1-490 

 1-503 

 1-517 

 1-531 

 1-546 

 1-560 

 1-575 

 1-590 

 1-605 

 1-621 

 1-636 

 1-652 

 1-668 

 1-685 

 1702 

 1-719 

 1-736 

 1-750 

 1-771 

 1-790 

 1-808 

 1-827 

 1-847 

 1-866 

 1-886 

 1-907 

 1-928 



The above Table is inaccurate for greater densities than 1*2 ; 

 this is obviated by a small additional weight which makes the 

 index point to zero when the glass rod is immersed in water ; 

 the above Table is then to be used by adding unity to the tan- 

 gent of the angle : the density is * 

 d=l + tan u. 



The balance may also be used for determining the coefficient 

 of expansion of liquids ; the density needs only determining for 

 two temperatures as different as possible. 



