282 REPORT—1862. 
Substituting now these expressions in (31) and integrating, we have 
du (du? . (dv\’ . (dw? 
~29=81 {255 +(cz) +(z) +(zz) | 
fi. dvu. (du\* (dv\? . (dw\? 
De pees pi et 
ae { aut (a) +(3) (Gi) } 
lw. (du? (dv\?_ (dw? 
96 
ti { Zatz) +(q) +(z) } (38 
4938 { rey eee du dvdv . dwdw jaar ) 
dz dy dy dz dy dz dy dz } 
dw. du dudu.dvdv. dwdw 
+26 | de Ge eda dzdx' dz =} 
lu dv .dudu. dvdv. dwdw 
og + 4 We 
a S| + atte ay dudy dx a} ’ 
which is exactly Green’s expression*, Green’s constants A, B... F answer- 
ing to Cauchy’s A, 34... Jf. The sum of the right-hand members of equa- 
tions (33) and (38) gives the complete expression for —2@ which belongs to 
Cauchy’s formule. It contains, as we see, 21 arbitrary constants, and is a 
particular case of the general form used by Green, which latter contains 
27 arbitrary constants. 
Thave been thus particular in deducing the form of Green’s function which 
belongs to Cauchy’s expressions, partly because it has been erroneously asserted 
that Green’s function does not apply to a system of attracting and repelling 
molecules, partly because, when once the function @ is formed, the short and 
elegant methods of Green may be applied to obtain the results of Cauchy’s 
theory, and a comparison of the different theories of Green and Cauchy is 
greatly facilitated. 
-* Cambridge Philosophical Transactions, vol. vii. p. 127. 
Fourth Report of the Committee on Steamship Performance. 
Report CONTENTS. 
Sheet of indicator diagrams of H.M.S. ‘ Colossus,’ ‘ Arrogant,’ and ‘ Hansa,’ and scale of 
displacement of the ‘McGregor Laird.’ 
Appendix, Table 1—Form of Engineers’ Pocket Log, issued by the Commiitee. 
Table 2.—Return of the particulars of the dimensions of 20 vessels in H.M. Navy, 
with the results of their trials upon completion for service. 
Table 3.—Table showing the results of the performances at sea, and when on trial, 
of H.M.S. ‘ Arrogant,’ ‘ Colossus,’ and ‘ St. George.’ 
Tables 4, 5, and 6.—Results of trials of H.M, screwships, officially tabulated by the 
Admiralty, in 1850, 1856, and 1861. 
Steam Transport Service.—Tables Nos. 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16 (the 
last 5 tables being summaries of the Tables 7 to 11) show the results obtained 
from vessels employed in transport service during the latter part of the Russian 
War, showing the respective values of the several steamships, classified according 
to the nature of the employment, or the special character of the duties required to 
be performed ; and giving, in addition, the cost of moving each ship 1000 miles, &e. 
Table 17.—Table showing performances of the Royal West India Mail Company’s 
Steamers from June 1861 to July 1862. 
Table mC imi of the indicator diagrams taken on all the voyages included 
in Table 17. 
