None
Vn+l - 1>n-l JC-Wn+l - ■Wn-l) v'n+l-v'n = dA' "n-l + Ul>n+1 - -Wn-l) = 1)' dA' - v' 11-309 17-204 5-735 5-701 5-608 + 0-093 8-609 4-179 2-077 1-048 0-527 0-258 2-836 1-393 0-692 0-349 0-176 0-086 2-820 1-401 0-691 . 0-352 0-169 0-092 2-788 1-387 0-696 0-344 0-175 0-083 0-032 + 0-014 -0-005 + 0-008 -0-006 + 0-009 0-128 0-043 043 0-040 -0-003 Sub-table c. v"„+i-v"n = dA" v' + v_ 2 dA" - v" -v" 11-483 11-295 + 0-183 5-704 5-591 + 0-113 2-811 1-389 0-696 0-350 0-174 0-085 2-780 1-391 0-695 0-345 0-171 0-086 + 0-031 -0-002 + 0-001 + 0-005 + 0-003 -0-001 0-048 0-043 0-000 Table VIIL RUBIDIUM IODIDE. RM = 212-5. Sub-table a. T = 19-5° C. V„+i~Vn=dA A -1000=11 dA-v 12-969 12-836 + 0-133 6-412 6-424 -0-012 3-221 3-203 + 0-018 1-601 1-602 -0-001 0-789 0-813 -0-024 0-391 0-422 -0031 0-204 0-218 -0-014 0-075 0-143 -0-068 0-082 0-061 + 0-021 Sub-table b. 1>n+l-1>n-l 4(»n+l - Vu-l) ^ v'n+l-v'n = dA' ■»»-! + i{Vn+l - V„-i) = v' dA' ~v' 12-884 19-381 6-460 6-470 6-414 + 0-056 9-633 3-211 3-205 3-209 -0-004 4-822 1-607 1-599 1-610 2-390 0-797 0-795 0-815 1-180 0-393 0-399 0-416 0-595 0-198 0-180 0-236 0-011 -0-020 -0-017 -0-056 +0-010 -0-009 0-279 0-093 0-123 0-113 0-157 0-052 0-052 0-061 Sub-table c. v"n+l-'V"„ = dA" t±JL=v" 2 dA"-v" 12-945 12-860 + 0-085 6-441 6-419 -0-022 3-213 1-600 0-792 0-395 0-192 099 3-206 1-606 0-814 0-419 0-227 0-128 0-007 -0-006 -0-022 -0-024 -0-035 -0-029 0-067 0-061 + 0-006 Table IX. CESIUM IODIDE. Csl = 260-0. T=19-5°C. Sub-table u. 'I'n+l — -Wn = dA A -1000 = '!) dA-v 14-893 14-788 + 0-105 7-445 7-343 -0-102 3-668 3-675 -0-007 1-S61 1-814 + 0-047 0-875 0-939 -0-064 0-456 0-484 -0-029 0-207 0-277 -0-070 0-042 0-235 -0-193 0-082 0-153 -0-071 Sub-table b. 1>n+l - 1>n-l JCn+l - '"n-l) v'n+\-1l'n = dA' ^»-l + 4(^n+l - V„-i) = v' dA' - v' 14-789 22-338 7-446 7-410 .7-379 11-113 3-704 3-722 3-657 5-529 1-843 1-806 1-851 + 0-031 +0-066 -0-046 -0-003 -0-069 -0-138 2-736 0-912 0-924 0-927 1-330 0-443 0-429 0-498 662 221 180 318 0-249 0-083 0-124 0-194 -0-070 0-124 0-041 0-041 0-163 -0-112 Sub-table c. i^"n-n--!'"n=rfA" 'i±l=^v" 2 dAl'-v" 14-893 14-788 + 0-105 7-427 7-361 + 0-066 3-695 3-666 + 0-029 1-834 0-899 0-442 0-194 0-083 1-832 0-933 0-491 0-297 0-214 + 0-002 -0-034 -0-049 -0-103 -0-131 0-061 0-163 -0 092 126 MR J. Y. BUCHANAN ON THE 52. Tables of Class F, illustrating the Method of arriving at the Volumetric Effect produced by changing the Concentration of a Solution. TRIAD OF CHLORATES. Table X. POTASSIUM CHLORATE. KC103 = 122-6. T=19-5°C. 1/4 11-352 1/8 5-632 7 6 5 4 3 2 1/16 1/32 1/64 1/128 1/256 1/512 2-786 1-337 0-661 0-324 0-158 0-057 1 1/1024 Sub-table A-1000 = i) dA ~v 11-352 5-720 5-632 + 0-088 2-847 2-785 + 0-062 1-448 1-337 + 0-111 0-676 0-661 + 0-015 0-337 0-324 + 0-013 0-166 0-158 + 0-008 0-101 0-057 + 0-044 StTB-TAELE 6. A{r„+i -■!!„_,) ^''n+i-v'n-dA' Vn-l + J(i;„+l-D„_i) = dA' - v' 11-352 5-711 5-641 + 0-070 8-567 4-295 2-124 1-013 0-503 0-267 2-855 1-432 0-708 0-338 0-168 0089 2-872 1-400 0-707 0-336 0-180 0-089 2-769 1-369 0-662 0-326 0-146 0-057 + 0-103 + 0-031 + 0-045 + 0-010 + 0-034 + 0-032 Sub-table c. V „+i - ■» ', v' + v_ ,, ~2 ^ dA'' - v'' = dA" 11-352 5-716 5-636 + 0-080 2-859 1-424 0-692 0-336 0-173 0-095 2-777 1-353 0-661 0-325 0-152 0-057 + 0-082 + 0-071 + 0-031 + 0-011 + 0-021 + 0-038 Tablb XI. RUBIDIUM CHLORATE. RbC103= 169-0. T = 19-5°C. Sue-table «,. Vn+l-Vn = dA A-1000 = y dA -V 12-726 6-373 6-353 + 0-020 3-170 3-183 -0-013 1-599 1-584 + 0-015 0-809 0-775 + 0-034 0-375 0-400 -0-025 0-200 0-200 0-000 0-089 0-111 -0-022 Sub-table 6. ■"n+i - ■».■-! i(»n+l- ''ii-l) v'„+i-v'„ = dA' l + Ufn+l-Vn-i)- dA' - v' 12-726 6-364 -0-002 9-543 3-181 3-190 3-174 + 0-016 4-769 2-408 1-184 0-575 1-590 0-803 0-395 0-192 1-596 0-783 0-403 0-185 1-578 0-795 0-392 0-207 + 0018 -0-012 + 0-011 -0-022 0-289 0-096 0-096 0-111 -0-015 Sub-table c. 6-368 6-353 + 0-010 3-180 1-597 0-796 0-389 0-193 0-092 3-178 1-581 0-785 0-396 0-203 0-111 + 0-002 + 0-016 + 0-011 -0-007 -0-010 -0-019 Table XII. C/ESIUM CHLORATE. Sub-table i CsC10j = 216-5. T=19-5°C. v„+i ~ v„ = dA A-1000 = w dA -V 14-515 7-282 7-233 + 0-049 3-564 3-669 -0-105 1-865 1-804 + 0-061 0-833 0-971 -0-138 0-495 0-476 + 0-019 0-184 0-292 -0-108 0-080 0-212 -0-132 Sub-table b. «n+l - V„-i i(('n + l-'!)n-l) 1''h+1- 0'n = dA' Vn -1 + i{l)n+l - V„-i) - v' dA' -v' 7-231 7-284 -0-053 10 3 3 3 + -846 -615 -670 -614 -056 5-429 1-810 1-744 1-870 -0-126 2-698 0-899 0-951 0-919 h 0-032 1-328 0-443 0-401 0-618 -0-117 0-679 0-226 0-218 0-300 -0-082 Sub-table c. v"n+\-v"n=dA" v' + v_ ,1 dA"-v" 14-515 7-267 7-258 -0-001 3-617 3-641 -0-024 1-804 0-892 0-448 0-201 0-084 1-837 0-945 0-497 0-296 0-212 -0-033 -0-053 -0-049 -0-095 -0-128 SPECIFIC GEAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 127 Tables of Class F, illustrating the Method of arriving at the Volumetric Effect produced by changing the Concentration of a Solution. TRIAD OF BROMATES. Table XIIL POTASSIUM BROMATE. KBrO, = 167-L T = 19-5°C. 7t m V 9 1/4 11-290 8 1/8 5-576 7 1/16 2-761 6 1/32 1-370 5 1/64 0-688 4 1/128 0-347 3 1/256 0-176 2 1/512 0-089 1 1/1024 Sub-table a. Vn-\-\ — l/'n = dA A -1000 = 11 dA-v 11-290 5-714 5-576 -[-0-138 2-815 2-761 -HO-054 1-391 1-370 -1-0-021 0-682 0-688 -0-006 0-341 0-347 -0-006 0-171 0-176 -0-005 0-087 0-089 -0-002 Stjb-tablb 6. Vn+l - 'i'n-l J(ll„+1 - Vn-l) v'n+l--l>'n = dA' 1>»-\ + i{rn+l-Vn-l) = v' dA'-v' 11-290 5-686 5-604 4-0-082 8-529 2-843 2-832 2-772 -1-0-060 4-206 1-402 1.393 1-379 •fO-014 2-073 0-691 0-691 0-688 -1-0-003 1-023 0-341 0-341 0-347 -0-006 0-512 0-171 0-172 0-175 -0-003 0-258 0-086 0-086 0-089 -0-003 Sub-table c. v"„+i-v"n = dA" 2 dA"-v" 11-290 5-700 5-590 -HO-110 2-824 2-766 -fO-058 1-392 1-374 -1-0-018 0-686 0-688 -0-002 0-341 0-347 -0-006 0-172 0-175 -0-003 0-086 0-089 -0-003 Table XI^ ". EUBI] DIUM BROMATE. Sub-table a EloBrC )3 = 213-5. T=19-5°C. Vn+l-Vn = dA A- 1000 = 1! dA-v 3-057 1-516 1-541 -0-025 0-774 0-767 4-0-007 0-360 0-407 -0-047 0-216 0-191 4-0-025 0-095 0-096 -0-001 Sub-table b. ■Kn+l - «n-l J(d„+i - ■i;„-i) v'„+i-v'„ = dA' ■"n-l -1- i( Wn4-1 -V„-i) = v' dA' - v' 3-057 1-527 1-530 -0-003 2-290 0-763 0-745 0-785 -0-040 1-134 0-378 0-402 0-383 4-0-019 0-576 0-192 0-183 0-200 -0-017 0-311 0-104 0-104 0-096 4-0-008 1 SUB-TABLB C. v"n+i-v\ = dA" 2 dA" - v'' 3-057 1-522 1-535 -0-013 0-759 0-776 -0-017 0-381 0-395 -0-014 0-200 0-195 -i- 0-005 0-099 0-096 4-0-003 Table X^ V. C^S] [UM BROMATE. Sub-table a CsBrOj- = 261-0. T=19-5° C. 1V-|-l-'!'n = <iA A -1000 = '!) dA-v 3-511 1-744 1-767 -0-023 0-903 0-864 -1-0-039 0-443 0-421 4-0-022 0-186 0-235 -0-049 0-101 0-134 -0-033 Sub-table b. V„+i-Vn-l v'n^l-v'n = dA' Vn-1 + j(«n-rl -V„-i) = v' dA'-v' 3-611 1-765 1-746 -1-0-019 2-647 0-882 0-876 0-870 4-0-006 1-346 0-449 0-425 0-445 -0-020 0-629 0-210 0-215 0-230 -0-015 0-287 0-096 0-096 0-134 -0-038 Sub-table t. r,"n+i-v"n = dA" dA"-v" 3-511 1-755 1-756 -0-001 0-889 0-867 4-0-022 0-434 0-433 4-0-001 0-201 0-232 -0-031 0-098 0-134 -0-036 :i28 MR J. Y. BUCHANAN ON THE Tables of Class F, illustrating the Method of arriving at the Volumetric Effect produced by changing the Concentration of a Solution. TRIAD OF lODATES. Table XVI. POTASSIUM lODATE. KI03 = 214-1. T = 19-5°C. n m V 9 1/4 8-832 8 1/8 4-339 7 1/16 2-189 6 1/32 1-096 5 1/64 0-584 4 1/128 0-269 3 1/256 0-127 2 1/512 0-057 1 1/1024 Sub-table u,. VnJr\-Vn = dA A-1000 = j) dA-v 8-832 4-493 4-339 -fO-164 2-150 2-189 -0-039 1-093 1-096 -0-003 0-512 0-584 -0-072 0-315 0-269 + 0-046 0-142 0-127 + 0-015 0-070 0-057 + 0-013 Sub-table i. v'n+l-1>'n=-dA' dA' - v' 8-832 4-429 4-403 -1-0-026 6-643 2-214 2-226 2-177 + 0-049 3-243 1-081 1 -058 1-119 -0-061 1-605 0-535 0-574 0-545 + 0-029 0-827 0-276 0-266 0-279 -0-013 0-457 0-152 0-151 0-128 + 0-023 0-212 0-071 0-071 0-057 + 0-014 Sub-table u. v"n+i-v"n = dA" ■»'+^-^'. 2 dA" -v" 8-832 4-461 4-371 -(-0-090 2-188 2-183 -1-0-005 1-076 1-107 -0-031 0-543 0-564 -0-021 0-290 0-274 + 0-016 0-147 0-127 + 0-020 0-070 0-057 + 0-013 Table X"V 11. EUi ilDIUM lODATE. Sub-table a EblOj = 260-5. T = 19-5'' C. ■i)n+l-Vn = dA A-1000=1) dA-v 2-576 1-300 1-276 + 0-024 0-615 0-661 -0-046 0-317 0-344 -0-027 0-154 0-190 -0-036 0-118 0-072 + 0-046 Sub-table 6. ^(Vn+l - Vn-l) v'n^X-v'n = dA' dA' - -b' 2-576 1-277 1-299 -0-022 1-915 0-638 0-644 0-655 -0-011 0-932 0-311 0-308 0-347 -0-039 0-471 0-157 0-184 0-163 + 0-021 0-272 0-091 0-091 0-072 + 0-019 Sub-table c v"„+i-v"n = dA" ■"' + ■" -v" 2 dA"-D" 2-576 1-289 1-287 + 0-002 0-629 0-658 -0-029 0-313 0-345 -0-032 0-169 0-176 -0-007 0-104 0-072 + 0-032 Table X :viii. c ^SIUM lODATE. Sub-table c CsIOg t. = 308-0. T = 19-5° C. Vw+l - V/i = ^A A-1000 = u dA-v 2-903 1-432 1-471 -0-039 0-685 0-786 -0-101 0-329 0-457 -0-128 0-185 0-272 -0-087 0-120 0-152 -0-032 Sue-table •). ■"'n+l- v'n = dA' '»n-l + l(Vn+l-Vn-l) = v' dA' - v' 2-903 1-411 1-492 -0-081 2-117 0-706 0-697 0-795 -0-098 1-014 0-338 0-352 0-443 -0-091 0-514 0-171 0-189 0-254 -0-065 0-305 0-102 0-102 0-152 -0-050 Sub-table e. lf'n+l-1>"n = dA" 2 dA"-v" 2-903 1-422 1-481 -0-059 0-691 0-790 -0-099 0-340 0-450 -0-110 0-187 0-263 -0-076 0-111 0-152 -0-041 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 129 Summary. § 53. Voluvietric Effect produced on changing the Concentration of a Solution. n m 9 1/4 8 1/8 7 1/16 6 1/32 5 1/64 4 1/128 3 1/256 2 1/512 1 1/1024 MR d^" -v". KCl RbCl CsCl + 0-159 + 0-185 + 0-209 + 083 + 0-090 + 0-102 + 0-037 + 0026 + 0-044 + 0007 + 0-017 + 0-025 - 0-008 + 0020 + 0020 + 0-002 + 0-009 + 0-015 -0-001 -0-035 + 0-004 -0-022 - 0-008 - 0-005 KBr RbBr CsBr + 0-133 + 0-232 + 0-144 + 0-061 + 0109 + 0-117 + 0011 + 0-035 + 0-034 -0-012 + 0001 + 006 -0-016 -0-011 - 0003 - 0-004 -0-022 -0-051 -0-003 -0031 -0039 - 0-008 ■-0-032 -0-011 -0-060 -0-014 KI Rbl Csl + 0-183 + 0-085 + 0-105 + 0113 + 0-022 + 0066 + 0-031 + 0-007 + 0029 -0-002 -0-006 + 0-002 + 0-001 - 0022 -0034 + 0-005 - 0024 -0049 + 0-003 - 0-035 -0-103 -0-001 -0-029 -0-131 0-000 + 006 -0-092 MRO3 d^"-v". KCIO3 RbC103 CSCIO3 + 0080 + 0-010 -0-001 + 0-082 + 0002 -0 024 + 0071 + 0-016 -0-033 + 0-031 + 0-011 - 0-053 + 0011 - 0-007 - 0-049 + 0-021 -0-010 -0095 + 0-038 -0-019 -0-128 KBr03 Rbl*-03 CsBr03 + 0-110 + 0-058 + 0-018 -0013 - 0-001 - 0-002 -0-017 + 0-022 -0-006 -0-014 + 0-001 -0-003 + 0-005 -0 031 -0003 + 0-003 -0-036 KIO3 RblOs CsIOg + 0-090 + 0-005 -0-031 + 0-002 -0-059 -0-021 -0-029 -0-099 + 0-016 -0-032 -0-110 + 0-020 - 0-007 -0-076 + 0013 + 0-032 -0-041 § 54. Solutions of the Salts of the Ennead MR. — The notes deal principally with the character of the change in the value of c?A — v with changes of the value of m in the dijGferent solutions. Table I. : — KCl. — This salt is the subject of the specimen table, § 50, and it has been commented on in connection with that table. Table II. : — RhCl. — In all three sub-tables the change of sign occurs between m= 1/128 and m= 1/256. There is a steady decrease in the positive values from m=l/4 to m= 1/128 in all three cases, excepting sub-table a at to =1/64, when an increase over the previous value occurs. The solutions of this salt show a regular decrease from high positive values of dA — i; to small negative values at low concentrations. Table III. :— CsCl. — The series of values of cZA — -u in the three sub-tables shows a very regular decrease in magnitude from m = 1/4 to to = 1/256 ; change of sign occurs between to= 1/256 and 1/512 with a small negative value. Table IV. : — KBr. — There is a rapid decrease in the value of dA — v from to= I/4 to TO =1/1 6, and between to =1/16 and to =1/32 there is change of sign to a small negative value, which persists right on to to =1/512, and which is the characteristic feature of the three sub-tables. TRANS. EGY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 17 130 MR J. Y. BUCHANAN ON THE It would seem to indicate that in the solutions of any concentration less than m= 1/64 the dissolution of a small quantity of salt produces the same increment of displacement. Table V. : — RhBr. — In sub-table a the value of d^ — v decreases very rapidly from 0"296 at m = 1/4, and changes to a negative value between m = 1/32 and m = 1/64, and then oscillates between alternate high negative values and low positive values. In sub-table c there is a regular increase in the negative values from m = 1/64 to m = 1/512. We have here definite evidence of expansion on dilution. Table VI.: — CsBr. — -The character of the decline in positive values for di^ — v is the same as that observed in the case of KBr and RbBr, and change of sign occurs between m= 1/16 and m= 1/32. After this there is an irregular oscillation between high positive and high negative values in sub-table o. In sub-table c the positive values persist to r/i= 1/32, after which change of sign occurs, and the negative sign remains for all values down to m= 1/512. The negative values reach a maximum at m= 1/128 and then decline. Here agaut. we have definite evidence of expansion. Table VII.: — KI. — A rapid decrease in positive values occurs between m=\jA. and ??i= ]/16. Then, with the exception of the small negative values of '01 8 and O'OIO at m = 1/32 and m = 1/512 respectively, there are small positive values for dA — v. This holds also in sub-table c, only that the positive and negative values foi' values of m below 1/32 are less. The final note for KBr applies with greater force in the case of KI. Table YIII. : — RhI. — In sub-table a there is a sudden fall from a high positive value of 0'133 for m.= l/4 to a negative value of 0'012 at m=l/8. and then a reversion to positive at 1/16 ; after this, the values are negative, except where m= 1/1024. In sub-table c there is a more progressive decrease in positive values from m = 1/4 to m = 1/16, and between this and «t = 1/32 there is change of sign. The negative values increase gradually to a maximum of 0-035 at i/256 and then decrease, and we have a positive value of 0-006 at 1/1024. The evidence of expansion is conclusive. The character of these values is com- parable with those of CsBr. Table IX. : — Csl. — In sub-table a, with the exception of the sudden fall to a negative value of 0-007 at m= 1/16, there is a progressive decrease to m= 1/32, where chano-e of sign occurs between m= 1/32 and m= 1/64, and an increase in magnitude of negative values to a maximum of 0-193 at m= 1/256, and then a slight fall. In sub-table c there is a progressive decrease in positive values to m = 1/32 ; then change of sign, and progressive increase in negative values to 0-131 where ot = 1/512, a slight decrease occurring at m= 1/1024. The character of values for di^-vm all three sub-tables is the same. This is the most marked instance where expansion occurs. SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 131 § 55. Solutions of the Salts of the Ennead Ifi^Og.— The reason for the small number of results in the cases of RbBrOg, RblOg, GsBrOg, and CsIOg is the very sparing solubility of these salts in water. Table X. : — KCIO^. — The values of dA — t; in all the sub-tables are positive. In sub-table a they are oscillatory in character, the maximum value being O'lll at m = l/32; the minimum of 0-008 at m= 1/256 rises to 0-044 at m= 1/512. In sub-table c the maximum occurs at m=l/l6, while the minimum is at m= 1/128. The nature of the oscillation is the same, but less pronounced. Table XL : — RhClO^. — There are somewhat irregular alternations between positive and negative values oid^ — v'va. the sub-table a. They are also of appreciable magnitude, and in sub-table c the oscillations are still apparent, although a definite change of sign occurs at m = 1/128, when the values of c?A — v for higher values of m are positive, and the lower values of m are negative. In the table for MR = RbCl the same character is observed as here in the sub-table c ; see note above. Table XII. : — CsClO^. — There are exhibited here regular alternations between com- paratively high positive values and high negative values for dA - v in sub-table a, except at m= 1/250 and m= 1/512, both of which are negative. The maximum positive value is at m = 1/32, while the maximum negative value is at TO= 1/64. Owing to the greater magnitude of the negative values than the positive ones in the sub-table a, we obtain a complete series of negative values of comparatively high magni- tude in sub-table c, and with the exception of a slight diminution in the negative value at m= 1/128 below that where m= 1/64, there is a progressive increase of the negative values from the beginning to the end, giving distinct evidence of expansion on dilution. Table XIII. : — KBrO^. — The character of changes in the values for dA — vm all three sub-tables is the same : a rapid fall in the positive values from 0-138 at m=l/8 to 0-021 where m= 1/32, the negative values from m= 1/64 onwards being negligible. This is observed in all three tables, although in sub-tables 6 and c the high magni- tude of the positive values for dA — -y is slightly modified. This feature of the steady fall in positive values to a series of negligible negative values is also to be seen in the series for ME = KBr, with the exception that there are two negative quantities of appreciable magnitude in the values for d^ — v, where m= 1/32 and m= 1/64 in sub-table c for KBr. Table XIV. : — RhBrO^. — In sub-table a there is a regular alternation between rather high negative values and positive values, while in sub-table c there is a regular transition from negative to positive values, the change of sign occurring at m= 1/256, the general character being that of commencing with a negative value and rising to a positive quantity. This is the only instance in these tables of the occurrence of contraction from the highest concentration, m— 1/32, to the lowest, m= 1/512. 132 MR ,T. Y. BUCHANAN ON THE Table XV. : — CsBrOg. — Here an irregular feature is observed in that there is a negative value of 0-023 at m=l/32, which changes to a positive value of 0-039 at m= 1/64, then a diminution in a positive value at m= 1/128 to the maximum negative value of the series of 0-049 at m= 1/256, with a slight diminution at m= 1/512. In sub-table c a similar series of values for dA — v is seen, except that they are more regular. Table XVI. ■.—KlO^.—ln sub-table a the high positive value of 0-154 for dA-v at m= 1/8 is changed to a negative value of 0-039 at m= 1/16, and with a diminution of the negative value to 0-003 at 1/32 the maximum negative value of 0-072 is reached at 771 = 1/64 ; then a transition occurs at m = 1/128 to a positive value of 0-046. After- wards the positive value falls away. There is thus a change from a high positive value to a high negative value, and then reversion to moderately high positive value. The same feature is observed in sub-table c, but it is of a more undulatory character. Table XVII. :— igfc/Og.— The positive value of 0-024 at m= 1/32 gives place to the maximum negative value of 0-046 at m= 1/64 ; then there is a diminution in negative values leading to a positive value of 0-046 at 1/512 in sub-table a. The same character is observed in sub-table c, only more regular, the maximum negative value of 0-032 occurring at to = 1/128. Table XVIII. : — Cs-JOg. — The values for dA-v in each of the three sub-tables constitute the most regular of all the series. All the values are negative and reach a maximum value at m= 1/128 in all three sub-tables, and fall away regularly for higher and lower values of m. The character of the values for CSIO3 somewhat resembles those for RblOg. Section IX. — Notes on the Values of v for the Enneads MR and MRO3. § 56. The increment of displacement produced in 1000 grams of water at 19-5° C, when 1/2 gram-molecule of potassium chloride is dissolved in it, is 14-001 Gj ; when a molecularly equivalent amount of potassium bromide is dissolved in the same quantity of water, the increase in the displacement is 17-547 Gt; when the salt in solution is potassium iodide, the number is 22-778 Gj. Replacing, therefore, the chlorine by bromine increases the displacement by 3-546 G.j^. ; and if the bromine be now replaced by iodine, there is a further increase of 5-231 Gt in the displacement; or, replacing the chlorine by iodine causes an increment of displacement of 8-777 Gj. Proceeding in a similar manner with the other salts of the ennead MR and tabulating the results, we obtain Table I. An inspection of the table shows us that the differences for Br — CI when equivalent quantities of the salts of K, Rb, and Cs are dissolved in the same quantity of water are of the same order of magnitude till m = 1/32. The same characteristic is observed between the same limits of m when bromine is replaced by iodine, but the differences for the same gram-molecular weight of the salt are in these three series greater than those observed when chlorine is replaced by bromine. In the third section SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 133 of the table, when chlorine is replaced by iodine, the numbers expressing the differences of the increments of displacement for the same value of m are the sum of the differences for Br— CI, I— Br. Turning now to Table II., we have the increase in the increment of displacement produced when the metal in combination with the same acid is varied. Here again it will be found that the numbers on the same line in each section are, inter se, of the same order of magnitude till m= 1/32, after which they vary more or less irregularly. Table I., giving the corresponding Differences between the Values of the Increments of Displacement, v, caused by the Dissolution of in gram-molecule of MBr and MCI; Ml and MBr; MI and MCt (where M = K, Rb, or Cs) in 1000 grams of Water at 19-5° C. ENNEAD MR. R = BROMI DE -CHLORIDE. IODIDE-BROMIDE. IODIDE-CHLORIDE. M = K. Eb. Cs. K. Rb. Cs. K. Rb. Cs. in. 1/2 3-546 3-625 3-249 5-231 5-543 6-031 8-777 9-168 9-280 1/4 1-791 1-781 1-690 2-591 2-853 3 032 4-382 4-634 4-722 1/8 0-898 0-884 0-813 1-260 1-483 1-541 2-158 2-367 2-354 1/16 0-469 0-436 0-398 0-619 0-747 0-802 1-088 1-183 1-200 1/32 0-240 0-216 0-241 0-314 0-380 0-348 0-554 0-596 0-589 1/64 0-131 0-138 0-091 0-141 0-186 0-244 0-272 0-324 0-355 1/128 0-061 0-070 0-102 0-069 0-114 0-091 0-130 0-184 0-193 1/256 0-041 0-067 0-080 0-029 0-029 0-053 0-070 0-096 0-133 1/51? 0010 0-017 0-029 0-015 0-053 0-127 0-025 0-070 0-156 1/1024 -0-021 0-090 Table II., giving the corresponding Differences between the Values of the Incre- ments of Displacement, v, caused by the Dissolution of m gram-molecule of RbR and KE; CsR and RbR; CsR and KR (where R = C1, Br, or I) in 1000 grams of Water at 19-5° C. ENNEAD ME. M = RUBIDIUM— POTASSIUM. CESIUM— RUBIDIUM. CESIUM— POTASSIUM. R = 01. Br. I. CI. Br. I. CI. Br. I. m. 1/2 14 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 2 636 1-303 0-641 0-336 0-155 0066 021 0-024 0009 2-715 1-293 0-627 0-303 0-140 0073 0-030 0-050 0-016 3-027 1-555 0-850 0-431 0-207 0-118 0-075 0050 0-064 0-021 3-764 1-864 0-932 0-455 0-219 0-115 0-053 0-022 0-006 3-388 1-773 0-861 0-417 0-244 0-068 0-085 0-035 0-018 -0-019 3-876 1-952 0-919 0-472 0-212 0-126 0-062 0-059 0-092 0-092 6-400 3-167 1-573 0-791 0-374 0181 0074 0-046 0-015 6-103 3-066 1-488 0-720 0-384 0-141 0-115 085 0-024 6-903 3-507 1-769 0-903 0-419 0-244 0-137 0-109 0-146 0-113 134 MR J. Y. BUCHANAN ON THE § 57. Tables III. and IV. deal with the salts of the ennead MRO3, and correspond in arrangement with Tables I. and II. respectively ; and what has been said of the two previous tables holds good, in general, with these two tables, but the agreement of the values is not so close, nor is the number of values tabulated so great. In Table III. the differences of the increments are nearly all negative quantities ; in Table IV. they are all positive. Table V. gives the differences of v between the oxyhalides and the halides of the same metal for the two enneads, MEO3 and MR, and here also the same characteristic agreement is noticed between the numbers on the same line in each section of the table. Having thus briefly explained the contents of the tables and the chief characteristics of the numbers in them, we will proceed to more fully discuss the effects produced on the displacement of 1000 grams of water at 19 '5" C. when the constituents of the salts dissolved in it are changed ; and in order to compare the results of the halides with those of the oxyhalides, we shall confine our attention to the numbers for >n= 1/16 and less. Table III., giving the corresponding Differences between the Values of the Incre- ments of Displacement, v, caused by the Dissolution of m gram-molecule of MBrOg and MCIO3 ; MIO3 and MBrOg ; MIO3 and MCIO3 (where M = K, Rb, or Cs) in 1000 grams of Water at 19-5° C. ENNEAD MRO,. R0.,= BROMATE— CHLORATE. lODATE— BROMATE. lODATE— CHLORATE. M = K. Rb. Cs. K. Rb. Cs. K. Rb. Cs. m. 1/2 1/4 -0-062 -2-458 -2-520 1/8 - 0-056 -1-137 -1-193 1/16 -0-024 -0-126 -0-158 -0-572 -0-481 -0-608 -0-596 -0-607 - 0-766 1/32 + 0033 -0-043 -0-037 -0-274 -0-265 -0-296 -0-241 -0-308 -0-333 1/64 + 0-027 - 0-008 -0-107 -0-104 -0-106 -0-078 -0 077 -0-114 -0-185 1/128 + 0-023 + 0-007 - 0-055 -0-078 -0063 + 0-036 -0055 -0-056 -0-019 1/256 + 0-018 -0 009 -0-057 -0-049 -0001 + 0-037 -0-031 -0-010 - 0-020 1/512 + 0-032 -0-015 -0-078 -0 032 -0-024 + 0-028 0-000 -0-039 -0-050 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 135 Table IV., giving the corresponding Differences between the Values of the Incre- ments of Displacement, v, caused by the Dissolution of m gram-molecule of RbROg and KRO^ ; CsROg and RbROg ; CsROg and KRO3 (where RO3 = CIO3, BrOg, or IO3) in 1000 grams of Water at l^'b" C. ENNEAD MRO,. M = RUBIDIUM— POTASSIUM. CAESIUM-RUBIDIUM. CESIUM— POTASSIUM. R03 = CIO3. BrOa. IO3. CIO3. BrOs. IO3. CIO3. Br03. IO3. m, 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1-374 0-720 0-398 0-247 0-114 0-076 0-042 0-054 0-296 0-171 0-079 0-060 0-015 0-007 0-387 0-180 0-077 0-075 0-063 0-015 1-789 0880 0-486 0-220 0-196 0-076 0-092 0-101 0-454 0-226 0-097 0-014 0-044 0-038 0-327 0-195 0-125 0-113 0-082 0-080 3-163 1-600 0-884 0-467 0-210 0-152 0-134 0-155 0-750 0-397 0-176 0-074 0-059 0-045 0-714 0-375 0-202 0-188 0-145 0095 Table V., giving the corresponding Differences between the Values of the Incre- ments of Displacement, v, caused by the Dissolution of m gram-molecule of MCIO3 and MCI ; MBrOg and MBr ; MIO3 and MI (where M = K, Rb, or Cs) in 1000 grams of Water at 19-5° C. MEO J— ME. R03- R= CHLORATE— CHLORI DE. BROMATE— BROMI DE. lODATE- IODIDE. M = K. Rb. Cs. K. Rb. Cs. K. Rb. Cs. m. 1/2 1/4 4-453 4-524 4-449 2-600 -2-449 1/8 2.-216 2-296 2-244 1-262 -1-235 1/16 1-101 1-163 1-194 0-608 0-601 0-638 -0-583 -0-727 -0-772 1/32 0-496 0-578 0-579 0-289 0-319 0-301 -0-299 - 0-326 -0-343 1/64 0-238 0-286 0-367 0-134 0-140 0-169 -0-111 -0152 -0-253 1/128 0-107 0-162 0-185 0-069 0-099 0-028 -0-078 - 0-078 -0-027 1/256 0-060 0-038 0-148 0037 002 0011 -0-041 - 0-028 - 0-005 1/512 - 0-007 0-038 0133 0-015 0-006 0026 -0032 -0-071 -0-083 § 58. If, in a solution containing I/I6 grm.-mol. KCl in 1000 grams of water at 19"5' C, we imagine the chlorine to be replaced by bromine, the process is accompanied by an increase of P"469 G^, in the displacement of the original solution. If the operation be performed upon an equivalent solution of RbCl, the increase in the displacement is 0"436Gt; if the salt in solution be I/I6 grm.-mol. CsCl, the increase is 0'398 Gt. Therefore, it appears that, when we replace CI by Br in 1/16 grm.-mol. solutions of the 136 MR J. Y. BUCHANAN ON THE chlorides of K, E,b, and Cs, approximately the same increment of displacement is produced. Commencing again with our solution of KCl, and replacing the potassium by rubidium, causes an increase m the displacement of 0-336 Gj ; when rubidium is replaced by caesium, the increase is 0'455Gt; replacing potassium by caesium produces an increase of 0'791 G^. If we now consider a solution of 1/16 grm.-mol. of KBr, and replace the potassium by rubidium, there is an increase in the displacement of 0'303 G^ ; replacing the rubidium by caesium causes a further increase of 0'417 Gt ; or if potassium be replaced by caesium, the increase is 0720 Gj. Setting out the numbers in the manner shown below gives a clearer view of the various changes that take place when one element in a compound is replaced by another : — K. Diff. Rb. Diff. Cs. V. f. V. CI . 1-684 + 0-336 = 2-020 + 0-455 = 2-475 Br . . 2-153 + 0-303 = 2-456 4-0-417 = 2-873 Diff. 0-469 0-436 0-398 It will be seen that the difference between RbCl and RbBr is nearly the same as that between KCl and KBr, because the increase in the increment of displacement produced when K is replaced by Rb in KCl is about the same as that produced when Rb takes the place of K in KBr. Therefore, when in solutions containing 1/16 grm.- mol. of KCl or KBr the potassium is replaced by rubidium, approximately the same increase in the increment of displacement is produced ; further, when CI is replaced by Br in KCl and RbCl, the increase is nearly the same in each case, but of a higher value than when the change is made in the metals. The difference between the atomic weights of CI and Br is 44'5 ; between K and Rb it is 46'4. The atomic weight of CI is less than that of K ; so, also, is the atomic weight of Br less than that of Rb ; yet there is a greater diflference of displacement produced by changing the acid than by changing the base. Turning our attention now to the chlorides and bromides of rubidium and caesium, we find that replacing CI by Br in RbCl causes an increase in the displacement of RbCl which is the mean of the increases produced when Cs replaces Rb in RbCl and RbBr, and is greater than when Br replaces CI in CsCl. There is a greater effect produced by changing the metals when CI is the acid than when Br is the acid ; also, when the acid united with the same base is changed, the variation is greatest for the lightest metal, and least for the heaviest. Proceeding on the hues set forth above, we will next consider the changes caused by replacing bromine by iodine, when combined with the same three metals : — IC. Di(f. Kb. Diff. Cs. «'■ !'. 11. Br . . 2-153 + 0-303 = 2-156 + 0-417 = 2-873 I . . 2-772 + 0-431 = 3-203 + 0-472 = 3-675 Diff. 0-619 0-747 0802 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 137 Replacing Br by I in KBr, RbBr, or CsBr produces increases in the displacements which become greater as the atomic weight of the metal increases. There is a greater increase produced by replacing K by Rb in KI than that produced when Rb takes the place of K in KBr; a similar effect is seen with the corresponding salts of rubidium and caesium, but in both instances the replacing of one metal by another causes a smaller change than when iodine takes the place of bromine in the bromide of the metal. The exchange of iodine for bromine produces increases in the values of v which rise with the increase of the atomic weight of the metal in combination ; as was previously observed, the replacement of chlorine by bromine caused changes in the increase of v which diminished with the increase in the atomic weight of the metal. We may summarise the foregoing observations by saying that tha replacement of the acid in a salt of the general formula MR (where M = K, Rb, or Cs, and R = CI, Br, or I) by another acid causes a greater change in the value of the displacement of a solution containing 1/16 grm.-mol. of the salt in 1000 grams of water at 19 '5° C. than the replacement of the metal by another metal. The only exceptions to this are when Cs takes the place of Rb in RbCl, and when Br replaces CI in CsCl, this latter being the smallest change produced when one acid is replaced by another. The values of the differences of the displacements for 1/16 grm.-mol. solutions of the salts of the halides are given in the table below. K. Diff. Rb. Diff. Cs. Ditr. (K by Cs). CI DiflF. Br DifF. I Diff.Clbyl 0-469 0-336 0-436 0-455 0-398 0-791 0-619 0-303 0-747 0-417 0-802 0-720 1-088 0-431 1-183 0-472 1-200 0-903 In the table, differences on the same line are, inter se, comparable ; the differences in the same column headed " Diff." are also comparable. § 59. The salts of the oxyhalides will now be dealt with in a manner similar to that of the halides. K. Diff. Eb. Diff. Cs. ClOg BrO, V. V. V. 2-785 + 0-398 = 3-183 + 0-486 = 3669 2-761+0-296 = 3057 + 0-454 = 3-511 Diff. -0024 -0-126 -0-158 If, in a solution containing 1/16 grm.-mol. KClOg per 1000 grams of water at 19'5°C., we replace the chlorine by bromine, the process is accompanied by a decrease in the displacement of the solution by an amount equal to — 0*024 G^ ; if the operation TEANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 18 138 MR J. Y. BUCHANAN ON THE be performed on an equivalent solution of RbClOg, the decrease is — 0"126 Gt; if the salt in solution be CsClOg, the decrease is —0-158 G^. Therefore, when we replace the chlorine by bromine in 1/16 grm.-mol. solutions of the chlorates of K, Rb, and Cs we observe that the change produces a decrease in the displacement of the solution, and this decrease becomes greater as the atomic weight of the metal increases. Confining our attention next to the changes produced in the displacement by varying the metal combined with the same acid, we find that when K is replaced by Rb in KClOg the displacement of the solution increases, as it also does when Rb is replaced by Cs in RbClOg. There is a similar increase when we consider the bromates of the same three metals ; but replacing K by Rb in KBrO^ produces a smaller increase than when the same change is made in KClOg. Similarly, the replacement of Rb by Cs in RbBrOg is less than when Cs replaces Rb in RbClOg. In the four cases where an exchange of metals takes place the corresponding changes in the displacements are positive ; with the three changes obtained by replacing CI by Br the changes in the displacement are negative, and numerically less than when the metals are changed. K. Diff. Rb. Diff. Cs. BrOs 10, v. V. 3-057 + 0-454 = 3-511 2-761+0-296 2-189 + 0-387 = 2-576 + 0-327 = 2-903 Diff. - 0-572 -0-481 0-608 With the bromates and iodates of the same three metals we find that replacing the bromine by iodine causes a reduction in the displacement of — 0'572 Gt in the case of KBrOg ; with RbBrOg the change in the displacement is — 0'481 Gt ; and with CsBrOg it is — 0'608 Gt. When we compare the results obtained by changing the metal combined with the same acid, we find that the iodates have positive values for the change in the displacement, just as the bromates and chlorates had, but that, whereas the replacement of Rb by Cs in RbClOg and RbBrOg gave an increase in the displace- ment which was greater than that produced by the exchange of Rb for K in KClOg and KBrOg, the replacement of Rb by Cs in RblOg causes an increase in the displacement which is less than that caused by replacing K by Rb in KlOg. The results of the changes produced in the displacement by the replacement of one constituent by K. Diff. Rb. Diff. Cs. Diff. (K by Cs). C103 Diff. BrOg Diff. IO3 DiffiClOgbylOg -0-024 0-398 -0-126 0-486 -0-158 0-884 -0-572 0-296 -0-481 0-454 -0-608 0-750 -0-596 0-387 -0-607 0-327 -0-766 0-714 SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 139 another in the salt dissolved is given in the preceding table. We do not here find so close an agreement between the numbers in a line, nor between those in the same column, but the agreement is still near enough to prevent any ambiguity as to which line or column a series belongs. Moreover, the columnar differences are all positive, while the line differences are all negative. We may further note that with the replace- ment of Eb by Cs and K by Cs the columnar differences decrease with an increase in the molecular weight of RO3, while replacing K by Rb causes irregular changes in the displacement. With the line differences the replacement of CIO3 by BrOj and ClOg by IO3 causes an increase with an increase of the atomic weight of the metal ; but with the replacement of BrOg by IO3 the changes in the displacement are irregular. § 60. The next effect to consider is that produced by the addition of the three oxygen atoms to the salts of the halides to form the corresponding salts of the oxyhalides. K. Kb. Cs. CIO3— CI . . MOl 1-163 1-194: BrOg— Br . . 0608 0-601 0-638 IO3— I . . -0-583 -0-727 -0772 in order to do this the above table has been constructed, in which the differences between the corresponding salts of the halides and oxyhalides for the same metal are entered in vertical columns. If we imagine that in a solution of 1/16 KCl-l- 1000 grams of water at 19-5° C. we add sufficient oxygen to the chloride and so produce KCIO3 in solution, the operation is accompanied by an addition to the displacement of I'lOl Gtt ; if the same operation be performed on a I/I6 grm.-mol. solution of the bromide of the same metal, the increase in the displacement is only 0'608 G^; and if we treat a solution of the iodide in the same way it produces a diminution in the dis- placement of —0-583 Gj. An inspection of the changes occurring when the three corresponding salts of rubidium and caesium are similarly treated shows us that they behave not only in an analogous manner, but that the amount of the change in each case is almost the same as that observed with the potassium salts, increasing slightly with the atomic weight of the metal. This action of the three atoms of oxygen upon the displacements of solutions of I/I6 grm.-mol. of the halides in 1000 grms. of water at 19-5° C. is peculiar, since in each case we have added the same weight of oxygen, namely, 3 grams, and the effects produced by it are similar in the salts with the same acid but different bases, but differ when the acid in combination with the same base is varied. §61.^ General Comparison and Summary of the Variation in the Values of the Mean Increment of Displacement for Dilute Solutions of Salts of the two Enneads MR and MRO^ {where M may he K, Rb, or Cs, and R may be CI, Br, or I). — This comparison includes: — (a) The variation produced by successive dilutions of a solution of an individual salt. (b) The character of the variation in the case of the whole series of solutions of salts of the two enneads. (c) The variation with the molecular weight. 140 MR J. Y. BUCHANAN ON THE The first point has been adequately dealt with in the immediately preceding section, and the two remaining ones will now be considered. The diagram on next page clearly shows the relations pointed out above, and the following are the more distinctive features which are illustrated. All the halide salts, with the possible exception of KI, have the property of causing expansion with dilution of their respective solutions, this expansion, in the case of the chlorides, being nearly proportional to the rise in the atomic weights of the base, as shown by the almost parallel march of the curves. In the case of the bromides the march is not so regular, the solutions of the rubidium and csesium salts inducing a greater relative expansion on dilution than is the case with the potassium salt, the change being greatest in the case of the rubidium salt. With the iodides, this increased effect of expansion which occurs on dilu- tion of solutions of the salts of rubidium and caesium over that of potassium is considerably enhanced, the solutions of potassium iodide showing practically no expansion. 