Royal Society. 147 



tings took root treated by the new method as had rooted by the old. 

 The mortality' in the open ground was increased by slugs having 

 eaten off above the soil some of the cuttings ; those thus damaged 

 were examined after they had been in the ground a month, and it 

 was found that the coUodion was quite as sound as when first ap- 

 plied. It would therefore appear that the collodion seals the wound 

 of the cutting, and protects it from the fatal effects of damp, until 

 roots are prepared to force through the covering of gun-cotton. It 

 is further stated, that the application of this solution has been found 

 to be exceeduigly beneficial in the pruning of such plants as Euphor- 

 bia speeiosa, Impatiens latifolia, Impatiens latifoUa-alba, Hoya bella. 

 Hoya imperialis, &c., the cut branches being prevented from bleeding. 



It is the author's intention next spring to follow out this experi- 

 ment, in budding and grafting, as he considers that it will also be 

 useful in this branch of horticulture. 



Gutta-percha, dissolved in aether, was in some instances substi- 

 tuted to heal the wounds caused by pruning ; yet owing to this so- 

 lution not drying as rapidly as collodion, the first, and sometimes 

 the second application was not sufficient. 



The effect of these solutions upon cut flowers was very marked. 

 Two branches were gathered as nearly alike as possible; to the 

 flower-stalks of the one, collodion was applied. These flowers 

 were placed in vases filled ^vith water; those coated over with 

 collodion began to fade in thirty-six hours, and many were quite 

 dead in three days ; whilst the flowers merely placed in water in the 

 ordinary manner remained fresh and healthy. Those that faded 

 soonest were Reseda odorata and Tropceolum majus, and those which 

 were least affected were Tagetes erecta and Senecio erubescens. 

 Dec. 22, 1852. — Thomas Graham, Esq., V.P., in the Chair. 



" On certain Properties of Square Numbers and other Quadratic 

 Forms, with a Table by which all the odd numbers up to 9211 may 

 be resolved into not exceeding four square numbers." By Sir 

 Frederick Pollock, F.R.S. &c. 



In examining the properties of the triangular numbers 0, 1, 3, 6, 

 10, &c., the author observed that every triangular number was com- 

 posed of four triangular numbers, viz. three times a triangular num- 

 ber plus the one above it or below it ; and he found that all the 

 natural numbers in the interval between any /wo consecutive triangular 

 numbers might be composed of four triangular numbers having the 

 sum of their roots, or rather of the indices of their distances from 

 the first terra of the series constant, viz. the sum of the indices of 

 the four trianguh;/ numbers which compose the first triangular 

 number of the < wo. 



Not being at that time aware of any law by which the series that 

 fills up the intervals could be continued, he subsequently turned his 

 attention to the square numbers as apparently presenting a greater 

 Tariety of theorems. He observed that if any four square numbers, 

 a», b*, c', rf•^ have their roots such, that, by making one or more 

 positive and the rest negative, tlie sum of the roots may be equal to 

 1 , then if the root or roots of which the sum is 1 less be each of 



